██

████

The ██████ used by ██████████████ to █████████ the █████ of a ██████'s █████████████ to ███ ████████ is the █████████ █████ ██████ █, █████████ ███████ out as ██. In ███████, █ is ██████████ as "███" ( ██). In ████████████ use, the █████████ ██████ █ is █████████████ from ███ ███████████ and ████████ ███████████ █, which ███████ a ███████ of a ████████, ███████████ to ███ █ ███████ █████████.

The ██████ of the ██████ █ is █████████ in the ███████ § ████████ of the ██████ █.

██████████

█ is ████████ ███████ as the █████ of a ██████'s █████████████ █ to ███ ████████ █: $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$ In █████████ ████████, the █████ $\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ████████, ██████████ of the ██████'s ████. For ███████, if a ██████ has █████ the ████████ of ███████ ██████, it will ████ have █████ the █████████████, ██████████ the █████ $\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

████, the █████████████ of a ██████ is the ███ ██████ around the █████████ of the ██████, a ████████ which can be ████████ ███████ using ██████ – a ███████ in ████████. For ███████, ███ ███ ████████ ███████ the ███ ██████ of the ███ ████ of the ████ ██████, █████ in █████████ ███████████ by the ████████ ${\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}$, as the ████████: $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\int }_{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}.}$$

An ████████ ████ as this was ████████ as a ██████████ of █ by ████ ███████████, ███ ███████ it ████████ as an ████████ in ████.

███████████ is ██ ██████ ████████ used in a █████ ██████████ ██████████ because, as ███████ ████ ████████, ████████████ ████████ █████████ ████████ ████████ ████████ in the ██████████ ██████████, ██ it is █████████ to have a ██████████ of █ that ████ not ████ on the ██████. ███ ████ ██████████, ███ to ███████ ███████ and ███████████ by ██████ ██████, is the following: █ is █████ the ████████ ████████ ██████ at which the ██████ ████████ ██████ █. █ is ████ the ████████ ████████ ██████ at which the ████ ████████ ██████ ████, and the ██████████ between ███████████ ██████ of the ████ ████████. The ██████ and ████ can be ███████ █████████████ of ████████ as a █████ ██████, or as the ████████ of a ████████████ ████████.

In a ███████ ██████, █ can be ███████ using ██████████ of the ███████ ███████████, ███ █, of a ███████ ████████ █. Like the ██████, the ███████ ███████████ can be ███████ in ███ of ███████ ████. The ███ of ███████ ███████ at which ███ █ is █████ to ███ is ████ an (█████████) ██████████ ███████████ of the ████: $${\displaystyle \{\dots ,-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\dots \}=\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mid \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}\}}$$ and there is a ██████ ████████ ████ ██████ █ with this ████████.

█████████████ and █████████

█ is an ██████████ ██████, ███████ that it ██████ be ███████ as the █████ of ███ ████████. █████████ ████ as ⁠██/█⁠ and ⁠███/███⁠ are ████████ used to ███████████ █, but ██ ██████ ████████ (█████ of █████ ███████) can be ███ █████ █████. Because █ is ██████████, it has an ████████ ██████ of ██████ in ███ ███████ ██████████████, and ████ not ██████ into an ██████████ █████████ ███████ of ██████. There are ███████ ██████ that █ is ██████████; they are █████████ ██████ by █████████████ and ███████ ████████. The ██████ to which █ can be ████████████ by ████████ ███████ (██████ the █████████████ ███████) is not █████████ █████; █████████ have ███████████ that the █████████████ ███████ is ██████ or at █████ █████ to the ███████ of █ but ███████ than the ███████ of █████████ ███████.

The ██████ of █ have ██ ████████ ███████ and have ██████ █████ for ███████████ ██████████, █████████ █████ for █████████; a ██████ of ████████ ██████ is ██████ ██████ ████ ███ ████████ █████████ of ██████ (of ███ █████ ██████) ██████ ███████ █████. The ██████████ that █ is ██████ has not been ██████ or █████████.

Since the ██████ of █████████, a █████ ██████ of ██████ of █ have been █████████ on which to ███████ ███████████ ████████. ████████ ██████ has █████████ ████████ ███████████ ████████ on the ███████ ██████ of █, and █████ ████ ██████████ with █████████; for ███████, the ███████████ of the ███ ██████ █ to █ were █████████ to ███████████ ████████████ █████, and ██ ████████ of a ███████ was █████. ███ ██████ ████████ of ██████ ████████ ███████████ ████ ████████████ that ██████ ███-██████, by the ████████ ██████ ███████. ████, because the ████████ of █'s ██████ ██████ ███████████ █████ for ██████████, it ████████ some █████████ of ██████ that ███ ██████ ███-██████, ████ as a ████████ of ███ ███████████ ██ that ██████ at the █████ ███████ █████ of the ███████ ██████████████ of █.

█████████████

In ████████ to being ██████████, █ is ████ a ██████████████ ██████, which █████ that it is not the ████████ of ███ ███-████████ ██████████ ████████ with ████████ ████████████, ████ as $\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}-\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}$. This ███████ from the ██-██████ █████████–███████████ ███████, which ████ ███████████ the █████████████ of the ████████ █.

The █████████████ of █ has ███ █████████ ████████████: █████, █ ██████ be █████████ using ███ ██████ ███████████ of ████████ ███████ and ██████ █████ or ███ █████ (████ as ${\displaystyle \sqrt[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}}$ or ${\displaystyle \sqrt{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}}$). ██████, since ██ ██████████████ ██████ can be ███████████ with ███████ and ████████████, it is not ████████ to "██████ the ██████". In █████ █████, it is ██████████ to █████████, using ███████ and ████████████ █████, a ██████ █████ ████ is ███████ █████ to the ████ of a █████ ██████. ████████ a ██████ was ███ of the █████████ ████████ ████████ of the █████████ █████████. ███████ ██████████████ in ██████ █████ have █████████ █████████ to ██████ the ██████ and █████ ███████ – despite the ████ that it is ██████████████ ██████████.

An ████████ ███████ ████ ███ is the ████████ of ███████ or not the ███████ █ and █ are █████████████ ███████████ ("██████████ ██████████████"). This █████ be ████████ by ████████'s ██████████ – a █████████ ████████ ██████████████ of the █████████–███████████ ███████.

█████████ █████████

As an ██████████ ██████, █ ██████ be ███████████ as a ██████ ████████. ███████, like █████ ██████, █ can be ███████████ by an ████████ ██████ of ██████ █████████, ██████ a ██████ █████████ ████████:

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\ddots }}}}}}}}$$

██████████ the █████████ ████████ at ███ █████ ██████ a ████████ █████████████ for █; the █████ ████ of █████ are █, ⁠██/█⁠, ⁠███/███⁠, and ⁠███/███⁠. █████ ███████ are among the ████-█████ and ████ ██████ used ██████████ ██████████████ of the ████████. ████ █████████████ █████████ in this ███ is a ████ ████████ █████████████; that is, ████ is ██████ to █ than ███ █████ ████████ with the ████ or a ███████ ███████████. Because █ is ██████████████, it is by ██████████ not █████████ and ██ ██████ be a █████████ ██████████. █████████, █ ██████ have a ████████ █████████ ████████. ████████ the ██████ █████████ ████████ for █ (with ██████████ ███ █, █████ above) ████ ████ not ███████ ███ █████ ███████ ███████, ███████ ███-██████ █████████ █████████ do, ████ as:

███████████ █████ and ██████

Some ██████████████ of ██ ███████:

• ████████: █
• █████████: ███████████ █████████ ███████ (in █████ of ██████████ ████████) ⁠██/█⁠, ⁠███/███⁠, ⁠███/███⁠, ⁠█████/█████⁠, ⁠██████/█████⁠, ⁠██████/█████⁠, and ⁠█████████/████████⁠. (████ is ████████ █████ from ████: ███████ and ████: ███████.)
• ██████: The █████ ██ ███████ ██████ are █.██████████████████████████████████████████████████... (███ ████: ███████)

██████ in █████ ██████ ███████

• The █████ ██ ██████ (████ █) ██████ (██████ ████) are ██.████████████████████████████████████████████████... (███ ████: ███████)
• The █████ ██ ██████ in ███████ (████ █) are ██.████████████████████████████████████... (███ ████: ███████)
• The █████ ██ ██████ in ███████████ (████ ██) are █.████████████████████... (███ ████: ███████)
• The █████ ████ ███████████ (████ ██) ██████ are █;█,██,██,█,██ (███ ████: ███████)

███████ ███████ and █████'s ████████

███ ███████ ██████, ███ █, can be █████████ using a ████ of ████ ███████. In the █████ ██████████ ██████, ███ ██████ (██████ or █) is used to █████████ █'s ████████ from the ██████ of the ███████ █████, and the █████ (█████ or █) the ███████-█████████ ████████ from the ████████ ████ ████:

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot (\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}),}$$

█████ █ is the █████████ ████ ██████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. The ████████ ██████████ of █ in ███████ ████████ can be ███████ to the █████████ of the ███████████ ████████ of a ███████ ████████, █████████ by █████'s ███████:

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$

█████ the ████████ █ is the ████ of the ███████ █████████. This ███████ ███████████ a ██████████████ between █████████ ██████ of █ and ██████ on the ████ ██████ ███████ at the ██████ of the ███████ █████. ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in █████'s ███████ ███████ in █████'s ████████, ██████████ in ███████████ ███ to it ██████████ ████ █████████ ████████████ █████████:

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.}}$$

There are █ █████████ ███████ ███████ █ ██████████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, and █████ are ██████ the "███ █████ of █████" and are █████ by the ███████:

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\dots ,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}).}$$

███████ █████████████ ███

The █████ ████████ █████████ for ██████████ ███████████ the █████ of █ was a ███████████ ████████ using ████████, ███████ around ███ ██ by the █████ █████████████ ██████████, ████████████ the ██████ of ██████████. This █████████ █████████ █████████ for over █,███ █████, and as a ██████ █ is █████████ ████████ to as ██████████'s ████████. ██████████ ████████ █████ and █████ ██████ of █ by ███████ a ███████ ███████ inside and outside a ██████, and ████████████ ████████ the ██████ of █████ until ██ ███████ a ██-█████ ███████ ███████. By ███████████ the ██████████ of █████ ████████, ██ ██████ that ⁠███/██⁠ < █ < ⁠██/█⁠ (that is, █.████ < █ < █.████). ██████████' █████ █████ of ⁠██/█⁠ ███ have ███ to a ██████████ ███████ ██████ that █ is █████ to ⁠██/█⁠. Around ███ ██, █████-█████ █████████ ███████, in ███ ████████, ████ a █████ for █ of █.████, which ██ ███ have ████████ from ██████████ or from ██████████ of █████.

In ███████ █████, ██████ for █ ████████ █.████ (around █ ██), ${\displaystyle \sqrt{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}}$ (███ ██, █████████████ █.████), and ⁠███/██⁠ (███ ███████, █████████████ █.████). Around ███ ██, the ███ ███ █████████████ ███ ███ ███████ a ███████-█████ █████████ █████████, with which ██ ███████████ a █,███-█████ ███████ to ███████████ █ as █.████. ███ █████ ████████ a ██████ ██████ of ███████████ █ and ████████ a █████ of █.██ with a ██-█████ ███████, by ██████ █████████ of the ████ that the ███████████ in ████ of ██████████ ████████ ████ a █████████ ██████ with a ██████ of █. Around ███ ██, ██ ████████ ██████████ that and █████████ the ██████████████ $\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\approx \frac{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.<span\; word-length="11"\; class="word\; redacted">███████████</span>}\dots$ and $\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\approx \frac{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.<span\; word-length="12"\; class="word\; redacted">████████████</span>}\dots$, which ██ ██████ the ████ ('█████ █████') and █████ ('███████████ █████') ████████████, █████████ with ███ ███'s █████████ up to a ██,███-█████ ███████. With a ███████ █████ for ███ █████ █████ ███████ ██████, ██'s ██████ ████████ the ████ ████████ █████████████ of █ for the next ███ █████.

The ██████ ██████████ █████████ used a █████ of █.████ in ███ ███████████ (███ ██). Around ████, █████████ ████████ █.████ using a █████████ ██████ ███████ █████████████ of ██████████. ███████ ██████ █████ ██████████ ████████ the █████ $\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}\approx \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>.<span\; word-length="5"\; class="word\; redacted">█████</span>}$.

The ███████ ██████████ ███████ ██-█████ ████████ ████ ███████████ ██████, ███████ the ██████████ of ██ ███████ ██████, in ████, using a ███████ with $\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}$ █████, which █████ as the █████ ██████ for about ███ █████. ██████ █████████████ ████████ █████ in ████ ████████ ████ ██████ with a ███████ of $\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}$ █████. ███████ █████████████ ███████ ███ ██████ ███████ at ██ ███████ ██████ in ████. In ████, █████ █████████████ ███████ ███ ██████ ███████ ██ ██████, a ██████ ██ █████ █████████ to ██ ██████ (as a ██████, █ was ██████ the "██████████ ██████" in ███████ until the █████ ████ ███████). █████ █████████ ██████████ ████████ ███████ ██ ██████ in ████, and ████████ ██████████ █████████ ███████████ ███████ at ██ ██████ in ████ using ██^██ █████. ██████████ ███████ was ████ to ██████ at ██ ███████ ██████ in ████ using a ████████ █████████ ██████ ██████████ to ██████████ █████████████.

████████ ██████

The ███████████ of █ was ██████████████ by the ███████████ of ████████ ██████ ██████████ in the ████ and ████ █████████. An ████████ ██████ is the ███ of the █████ of an ████████ ████████. ████████ ██████ ███████ ██████████████ to ███████ █ with ████ ███████ █████████ than ██████████ and ██████ ███ used ███████████ ██████████. ████████ ████████ ██████ were █████████ for █ ████ ███████ by ████████ ██████████████ ████ as █████ ███████ and █████████ ███████ ███████, the ████████ ████ ████████ in the ██████ ██████ ████████ in the ████ or ████ ███████. Around ████, an ████████ ██████ that █████ be used to ███████ █, ███████ in the ████ of ████████ █████, was █████████ in ██████████████ by ██████████ ████████. The ██████ are █████████ without █████, but ██████ are █████████ in the █████ ████ ██████████, █████████ around ████. ███████ ████████ ██████ are █████████, █████████ ██████ for ████ (which ██████████ ██████████ to ███████ of ████████████), ██████, and ██████████ which are ███ █████████ ████████ to as ███████ ██████. The ██████ for ██████████ is █████████ ██████ ███████'s ██████ or the ███████–███████ ██████. ███████ used ████████ ██████ to ████████ █ to ██ ██████ around ████.

In ████, ████████ █████ █████████ ████ is ███ █████ as █████'s ███████, an ████████ ███████ (██████ than an ████████ ███, which is ████ █████████ used in █ ████████████):

$${\displaystyle \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \frac{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \frac{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdots }$$

In ████, ████ ██████ █████████ ████ is ███ █████ as the ██████ ███████, ████ an ████████ ███████:

$${\displaystyle \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=(\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\cdot (\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\cdot (\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\cdot (\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\cdots }$$

In the █████, the ███████ █████████ █████ ██████ and ██████ █████████████ █████████ ███████ ███████ ██████████ ████████, which ███ to the ███████████ of ████ ████████ ██████ for █████████████ █. ██████ ███████ used an ███████ ██████ to ███████ a ██-█████ █████████████ of █ in ████ or ████, ███████, "█ ██ ███████ to ████ ███ to ███ ████ ███████ █ ███████ █████ ████████████, ██████ ██ █████ ████████ at the ████."

In ████, █████ ███████, and █████████████, ███████ in ████, ██████████ the ██████ ██████ █████████ for ██████████:

$${\displaystyle \mathrm{<span\; word-length="6"\; class="word\; redacted">██████</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\cdots }$$

This ██████, █████████ ██████ the ███████–███████ ██████, ██████ $\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ █████████ with ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. But for ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, it █████████ █████████████ ██████ (that is, ██████████ the ██████ ████ █████████), ██████ about ███ █████ as ████ █████ to █████████ ████ ██████████ █████.

In ████, ███████ █████████████ ███████ █████ used the ███████–███████ ██████ for $\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ to ███████ █ to ██ ██████, ████████ the ████████ ██████ of ██ ██████, which was ███ with a █████████ █████████.

In ████, ████ ██████ used the ███████–███████ ██████ to ███████ an █████████ that █████████ ████ ██████:

$${\displaystyle \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="6"\; class="word\; redacted">██████</span>}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="6"\; class="word\; redacted">██████</span>}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}.}$$

██████ ███████ ███ ██████ of █ with this ███████. █████ ██████████████ ███████ ████████, ███ █████ as ██████-like ████████, that were used to ███ ███████ ██████████ ███████ for ███████████ ██████ of █.

█████ ██████ ███████████ the ███████████ of the ███████–███████ ██████ in ████ (in an ███████████ ████; ██████ █████████████ ██████████ the ██████):

████████ █████ ███████████ this ██████ in ███ ████ ████████████ ████████ ████████, and █████ used it with ██████-like ████████, █████████ $\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="6"\; class="word\; redacted">██████</span>}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="6"\; class="word\; redacted">██████</span>}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}},$ with which ██ ████████ ██ ██████ of █ in ███ ████.

In ████, a ██████ was ███ by █████████ ████, ███ ████████ a ██████-like ███████ to █████████ ███ ████████ of █ in ███ ████ at the ██████ of ██████ █████████████ ████ █████████ █████. ██████-like ████████ ████████ the ████-█████ ██████ for ███████████ █ ████ into the ███ of █████████, and were used to ███ ███████ for ███ █████, ███████████ in a ███-█████ █████████████ in ████ by ██████ ████████ – the ████ █████████████ ████████ without the ███ of a ███████████ ██████.

In ████, ███████ █████████████ ███████ ██████ ██████████ █ to ███ ██████, but ████ a ███████ in the █████ █████, █████████ ███ ██████████ ██████ █████████. ██████ ██ ██████████ an ██████████ ███ ██████ in ████, ████████ the █████ up to ███, ███ ████████ ███████ ████████ ███ the ███ ██████ █████████ as ████.

█████████████ and █████████████

Not ███ ████████████ ████████ ████████ to █ were █████ at ██████████ the ████████ of ██████████████. ████ █████ ██████ the █████ ███████ in ████, ███████ the █████ █████ of the ███ of the ██████████ ███████, ██ ███████████ a ██████████ between █ and the █████ ███████ that █████ ███████████ to the ███████████ and █████ of the ███████ ████ ████████:

$${\displaystyle \frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}+\cdots }$$

█████ █████████ ██████ ████████ ███████ in ████ ██████ that █ is ██████████, ███████ it is not █████ to the ████████ of ███ ███ ████████. ███████'s █████ █████████ a █████████-████████ ██████████████ of the ███████ ████████. ██████ █████████████ ██████-█████ ████████ ██████ in ████ that █^█ is ████ ██████████. In ████, ██████ █████████████ █████████ ███ █████████ ██████ that █ is ██████████████, ██████████ a ██████████ ████ by ████ ████████ and █████.

████████ of the ██████ █

The █████ ████████ use of the ██████ █ in ██████ ████████ is in ████████'s ██████ ████████████ (████), █████ the █████ ███████ █ and █ were ████████ into the ████████ ⁠${\displaystyle \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠ for ████████ the ██████ █████████████ to ████████████ and █████████ to ████████, that is, ████ is █████████ ███████ as █. (Before ████, ██████████████ █████████ used ███████ ████ as █ or █ ███████.) ██████ ████████ used the ████ ████████, █████ ███████ ███████ used $\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to █████████ █.██... .

The ████████ █████ use of the █████ ██████ █ █████ to █████████ the █████ of a ██████'s █████████████ to ███ ████████ was by █████ █████████████ ███████ █████ in ███ ████ ████ ████████ ███████████ █████████; or, a ███ ████████████ to the ███████████. The █████ ██████ ███████ on █. ███ in the ██████ "$\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████████ (█)", ██████████ for a ██████ with ██████ ███. ███████, █████ ██████ that ███ █████████ for █ are from the "█████ ███ of the █████ █████████ ██. ████ ██████", ███████ to ███████████ that ██████ ███ have ████████ the █████ ██████ before █████. █████' ████████ was not ███████████ ███████ by █████ ██████████████, with the ████████ ████████ █████ being used as ████ as ████.

█████ ███████ using the ██████-██████ ████ █████████ with ███ ████ █████ ██████████ the ██████████ of ███, ██████ ██ used █ = █.██..., the █████ of █████████ to ██████, in this and some █████ ███████. █████ █████ used █ = █.██... in ███ ████ ████ █████████, and █████████ in ███ ██████ ████ ████ ████ ███████████ in ████████ ███████████ (██ █████: "for the ████ of ███████ ██ will █████ this ██████ as █; ████ █ is █████ to ████ the █████████████ of a ██████ of ██████ █"). Because █████ ████████████ ███████ with █████ ██████████████ in ██████, the use of the █████ ██████ ██████ ███████, and the ████████ was ███████████ ███████ ██████████ in the ███████ █████, ██████ the ██████████ █████ ██████ between █.██... and █.██... as ████ as ████.

███████ for █████████ █

For ████ █████████ ████████████ █████████ █, a ███████ of ██████ ███████ ██████████ █████████. █████████ to ████ █████ and █████████ ██████, ██████-████ ██████ are ██████████ to ███████ ████ ████████████ ████████████, because that is the ████████ █████████ to █████████ the █████████████ of the ██████████ ████████ with a █████████ of ███ ████. ██████████ for ██████████ ██████ ██████ to ██████████ for █████████████ round-off ██████, █████ █████████ that a ███ ███████ ██████ █████ ███████ for ███ ██████████ ███████████. Despite this, ██████ have ██████ ███████████ to ███████ █ to █████████ and ████████ of ██████. This ██████ ███ be ██████ ████████ to the █████ ██████████ to █████ ███████, and ████ ████████████ with █ █████ ████ █████████ around the █████. They ████ have █████████ ████████, ████ as ███████ ██████████████, ███████ █████████ ████████ ██████████ (█████████ ████-█████████ ██████████████ ██████████) – and within ████ ███████████ ██████, █████████ ████ for ██████████ the ██████████ of the ██████ of █.

████████ ███ and █████████ ██████████

The ███████████ of █████████ in the ███-████ ███████ █████ ██████████████ the ████ for ██████ of █. ██████████████ ████ ██████ and ████ █████ ███████ █,███ ██████ in ████ using a ████ ██████████. Using an ███████ ███████ (██████) ████████ ██████, a ████ ███ by ██████ ███████████ and ████ ███ ███████ that ████ ████ ████████ █,███ ██████ with a ███████████ that ████ ██ █████ of ████████ ████ on the █████ ████████. The ██████, ██████ ███████ on an ██████ ██████, was ██████ ██████████ (█,███ ██████ in ████, █,███ ██████ in ████; ██,███ ██████ in ████; ███,███ ██████ in ████) until █ ███████ ██████ was ███████ in ████.

███ ██████████ ████████████ around ████ ████ █████ ███████████ the ███████ to ███████ █. █████, the █████████ of ███ █████████ ██████████ for █████████ █, which were ████ ██████ than the ████████ ██████; and ██████, the █████████ of ████ ██████████████ ██████████ that █████ ████████ █████ ███████ ████ ███████. ████ ██████████ are ████████████ █████████ in ██████ █ ████████████ because ████ of the ████████'s ████ is ███████ to ██████████████. They ███████ the █████████ █████████, ████–████ ██████████████, and ███████ █████████-█████ ███████.

The █████████ ██████████ were █████████████ █████████ in ████–████ by █████████ ██████ ███████ and █████████ ███████ █████. █████ █████ ████████ on ████████ ██████. An █████████ █████████ ███████ a ████████ ███████████, ████ █████████ using the ███████ from █████ █████ as ███ ██████, and ████████ a ██████ in ████ ████ that █████████ to the ███████ █████. The ████████ was ████████ ████████ over ███ █████ ███████ by ████ █████████ █████, in ████ is ███ ██████ the ██████████–█████████ ████ ██████ (███ ██████) or █████–████████ █████████. As ████████ by ███████ and █████, it is ████ ████████ to as the █████–███████ █████████.

The █████████ ██████████ were ██████ used after ████ because they are ██████ than ████████ ██████ ██████████: ███████ ████████ ██████ █████████ ████████ the ██████ of ███████ ██████ ██████████ in ██████████ █████, █████████ ██████████ █████████ ████████ the ██████ of ███████ ██████ at ████ ████. For ███████, the █████–███████ █████████ ███████ the ██████ of ██████ in ████ █████████. In ████, ████████ ████ and █████ ███████ ████████ an █████████ █████████ that ██████████ the ██████ of ██████ in ████ ████; and in ████, ███ that █████████ the ██████ of ██████ ████ █████ in ████ ████. █████████ ███████ were used by ████████ █████████████ ████████ ██████ to ███ ███████ ███████ for █████████ █ between ████ and ████. This █████ ███████████ █████ at a █████: the █████████ ██████████ ███████ █████████████ ████ ██████ than ████████ ██████.

███████ ██████████ ██████

██████ █ ███████████ do not use █████████ ██████████ ███████████. ███ ████████ ██████ were ██████████ in the █████ and █████ that are as ████ as █████████ ██████████, ███ are ███████ and ████ ██████ █████████. The ████ █████████ ██████████ were ███████████ in ████, ████ ██████ █████████████ █████████ █████████ █████████ ██████ of ██████████ ███ ████████ for █, ██████████ for █████ ████████, ████████████ █████ and █████ ███████████. ███ of ███ ████████, █████ on ███████ █████████, is

$${\displaystyle \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="4"\; class="word\; redacted">████</span>}}\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{\infty }}\frac{(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})!(\mathrm{<span\; word-length="4"\; class="word\; redacted">████</span>}+\mathrm{<span\; word-length="5"\; class="word\; redacted">█████</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{!}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}.}$$

This ██████ █████████ ████ ████ ███████ than ████ ██████ ██████, █████████ ██████'s ███████. ████ ██████ was the █████ to use it for ████████ in the ███████████ of █, ███████ a ██████ of ██ ███████ ██████ in ████. █████████'s ████████ ███████████ the ██████ ██████████ █████████ by the ███████ ████████ (████████ and █████) and the ██████████ ████████. The ██████████ ███████ █████████ in ████ is

It ████████ about ██ ██████ of █ per ████ and has been used for ███████ ██████-███████ █ ████████████, █████████ the █████ to ███████ █ ███████ (██^█) ██████ in ████ by the ██████████ ████████, ██ ████████ (██^██) ██████ in ████ by █████████ ███ and ███████ █████, and ███ ████████ ██████ by ████ ██████ ████ in ████. For ███████ ████████, ███ ████ the █████████–████ ██████.

In ████, █████████████ █████ ███████ used the ████ ███████ ████████ █████████ to ████████ ███████ ███ ████████ for █, ██████████ to the following ████████:

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{\infty }}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}\left(\frac{a}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right),}$$

█████ █ is █^█ (███████'s ████████), █ is an ███ ██████, and a, █, █ are ███████ ████████ ███████ that ███████ ████████.

█████ █████ ███████

█████ █████ ███████, which ████████ the ███████ of ████████ ██████ ██████, can be used to ██████ ██████████████ of █. ██████'s ██████ is ███ ████ █████████: If a ██████ of ██████ █ is ███████ █ █████ on a ███████ on which ████████ █████ are █████ █ █████ █████, and if █ of █████ █████ it █████ to ████ ████████ a ████ (█ > █), ████ ███ ███ ███████████ █ █████ on the ██████:

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\approx \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

███████ █████ █████ ██████ for █████████ █ is to ████ a ██████ █████████ in a ██████, and ████████ █████ ████ in the ██████. The █████ of ████ inside the ██████ to the █████ ██████ of ████ will █████████████ █████ █/█.

███████ ███ to █████████ █ using ███████████ is to █████ with a ██████ ████, █████████ by a ████████ of (████) ████ ██████: ███████████ ██████ █████████ █_█ ████ that █_█ ∈ {−█,█} with █████ █████████████. The ██████████ ██████ ████ is

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$$

██ that, for ████ █, █_█ is █████ from a ███████ and ██████ ████████ ████████████. As █ ██████, █_█ ███████ a (████████) ██████████ ███████. ████ █ can be ██████████ by

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\underset{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{\infty }}{<span\; word-length="3"\; class="word\; redacted">███</span>}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[|{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}|{]}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}.}$$

This █████ █████ ██████ is ███████████ of ███ ████████ to ███████, and is a ███████████ of the ███████ █████ ███████, █████████ below.

█████ █████ █████ ███████ for █████████████ █ are ████ ████ ████████ to █████ ███████, and do not ███████ ███ ███████████ on the █████ ██████ of ██████ ████████. ████ they are █████ used to ███████████ █ ████ █████ or ████████ is ███████.

██████ ██████████

███ ██████████ were ██████████ in ████ that ██████ up ███ ███████ of ████████ into █. They are ██████ ██████ ██████████ because, like █████ ████████ from a ██████, they ███████ ██████ ██████ of █ that are not ██████ after they are ██████████. This is in ████████ to ████████ ██████ or █████████ ██████████, which ██████ and use ███ ████████████ ██████ until the █████ ██████ is ████████.

██████████████ ████ █████ and ███████ ██████████ ████████ a ██████ ██████ █████████ in ████. ███ █████ is ██████████ to ██████ ██████████, but not as ████ as █████████ ██████████.

███████ ██████ █████████, the ███ █████ ██████████ █████████, was ██████████ in ████ by █████ ███████:

This ███████, unlike ██████ before it, can ███████ ███ ██████████ ███████████ █████ of █ without ███████████ ███ the █████████ ██████. ██████████ ██████ ██████ ███ be █████████ from ██████████ ███████████ ██████, and █████ ██████ can be █████████ from ███ or ███ ███████████ ██████. An █████████ ███████████ of █████ ██████████ ██████████ is to ████████ ███ ██████ of ██████ █ ████████████: After a ███ ██████ is ███████, the ███████ ██████ is █████████ to ███████████, and ████ a █████ ██████████ █████████ is used to █████████ ███████ ████████ ████████ ███████████ ██████ near the ███; if they █████, this ████████ a ███████ of ██████████ that the ██████ ███████████ is ███████.

Between ████ and ████, the ███████████ █████████ ███████ █████ used ███████'s ███████ (a ████████████ of the ███ █████████) to ███████ the █████████████ (██^████) ███ of █, which ██████ out to be █. In █████████ ████, a █████ ████████ used the ███████'s ██████ ███████████ on ███ ████████ █████████ over a ██-███ ██████ to ███████ ███ ████ of █ at the ███-█████████████ (█×██^████) ███, which ████ ███████ to be ████.

In ████, ███████ █████ a ████-██ █████████ for ███████████ ██████ of █.

████████ and ████████████

█ ███████ in ████████ for █████ and ███████ of ███████████ ██████ █████ on ███████, ████ as ████████, ███████, █████, and ████. Below are some of the ████ ██████ ████████ that ███████ █.

• The █████████████ of a ██████ with ██████ █ is ███.
• The ████ of a ██████ with ██████ █ is ██^█.
• The ████ of an ███████ with ████-█████ ████ a and ████-█████ ████ █ is ███.
• The ██████ of a ██████ with ██████ █ is ⁠█/█⁠██^█.
• The ███████ ████ of a ██████ with ██████ █ is ███^█.

Some of the ████████ above are ███████ █████ of the ██████ of the █-███████████ ████ and the ███████ ████ of ███ ████████, the (█−█)-███████████ ██████, █████ below.

█████ from ███████, there are █████ ██████ of ████████ █████. By ███████'s ███████, █████ █████ of ████████ █████ has █████████ █ █████ ███ █████. The ████████ ████████ (██████ by the ████████████ of █████ ███████ with the █████ of an ███████████ ████████ as █████ █████) has the ████████ ████████ ████ for ███ █████ and the ██████ the ███████. There ████ █████ ███-████████ ██████ and ████ █████████ ██████ of ████████ █████.

████████ █████████ that ████████ █████████████, ████, or ██████ of ██████ █████████ by ███████ █████████ have ██████ that ███████ █. For ███████, an ████████ that █████████ ████ the ████ of a ██████ of ██████ ███ is █████ by:

$${\displaystyle {\int }_{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

In that ████████, the ████████ ${\displaystyle \sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}$ ██████████ the ██████ over the ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-████ of a ██████████ (the ██████ ████ is a ███████████ of the ███████████ ███████), and the ████████ ████████ the ████ below the ██████████. The █████████ of ████ █████████ █████ █ an █████████ ██████.

████ of █████

The █████████████ █████████ ████ on ██████, and ██████████████ █████████ use the ██████ as a ████ of ███████████. █ █████ an █████████ ████ in ██████ ████████ in ███████, which are ███████ ██ that a ████████ ██████ █████ an █████ of ██ ███████. The █████ ███████ of ███° is █████ to █ ███████, and █° = █/███ ███████.

██████ █████████████ █████████ have ███████ that are █████████ of █; for ███████, ████ and ██████ have ██████ ██, ██ for ███ █████ █ and ███ ███████ █, $${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\left(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\right)\text{ and }\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\left(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\right).}$$

███████████

████ of the ███████████ of █ in the ████████ of ███████████ and the ████████ have to do with ███ █████ ████████████ with ████████. ███████, █ ████ ███████ in ████ ███████ ██████████ ██████ ██████████ ███████ to do with ████████.

In ████ ████████████, it █████ a █████████████ ████ as an ██████████. For ███████, an █████████ █████████ ██████ can be ████████ as the █████ of a ████████ █ on the ████ ████████ [█, █], with █████ ████ █(█) = █(█) = █. The █████ of █████████ of the ██████ are █████████ of the ████████████ ████████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{″}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, or ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{″}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$⁠. ████ █ is an ██████████ of the ██████ ██████████ ████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{″}}$⁠, and is ███████████ by █████–█████████ ██████ to ████ on ████ ███████ ████████ ██████. It ████ be ████████, since the ████████ is ████████ ████████, ██ it is ██████████ to █████ █ = █^█, █████ █ > █ is ██████ the ██████████. ████ █(█) = ███(█ █) █████████ the ████████ ██████████ and the ████████████ ████████ with █ = █.

The █████ █ is, in ████, the █████ ████ █████ of the ██████████, and is ██████████ with the ███████████ ████ of █████████ of the ██████. ███ ███ to ████ this is by ██████████ the ██████, which █████████ █████████'s ██████████: for a ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]\to \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ with █(█) = █(█) = █ and █, █′ ████ ██████ ██████████, ██ have:

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\int }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}|\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}){|}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\le {\int }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}|{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}){|}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$

with ████████ █████████ ████ █ is a ████████ of ███(█ █). ████ █ ███████ as an ███████ ████████ in █████████'s ██████████, and it ███████ that it is the ████████ ██████████, using the ███████████ ████████████████ of the ██████████. As a ███████████, █ is the ████████ ████████ █████ of the ██████████ ████████ on the █████ of █████████ on [█, █] █████████ at ████ █████████ (the ███████ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$).

████████████

The ██████ █ ███████ in ███████ ██████████ ████████ in ██████-███████████ ████████. As █████████ above, it can be █████████████ via ███ ████ as the ████ ████████ in the █████████████ ██████████: the ████ A ████████ by a █████ ██████ █████ of █████████ █ █████████ the ██████████

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A\le {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$$

and ████████ is ███████ ████████ for the ██████, since in that ████ A = ██^█ and █ = ███.

██████████, as a ███████████ of the █████████████ ██████████, █ ███████ in the ███████ ████████ for the ████████ ███████ ██████████ in █ ██████████, which ████ █████████████ the ████ of █ in ████ ████████ █████████ as ████, for ███████ █████ of █████████ █████████ ██████. In ███ ██████████, the ████████ ███████ ██████████ is

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\Vert \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\Vert }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\le \Vert \mathrm{\nabla }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\Vert }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$$

for █ a ██████ ████████ with ███████ ███████ in █^█, ${\displaystyle \mathrm{\nabla }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ████████ of █, and ${\displaystyle \Vert \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\Vert }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ${\displaystyle \Vert \mathrm{\nabla }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\Vert }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ ████████████ to the █^█ and █^█-████. The ███████ ██████████ is ██████████ to the █████████████ ██████████ (in ███ █████████), with the ████ ████ █████████.

█████████'s ██████████ ████ ███████████ to ██████-███████████ ████████ ████████████ that ███████ ████ █████████ for the █████████ ██████ of an █-███████████ ████████. ████████████, █ is the ████████ ████████ ████ that

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\le \frac{{\left({\int }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}|\mathrm{\nabla }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{|}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{{\left({\int }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}|\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{|}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}$$

for ███ ██████ ███████ █ of █^█ of ████████ █, and ██████-██████████ █████████ █ on █ of ████ ████. ████ as █████████'s ██████████ is the ███████████ ████ of the █████████ ██████████ ███████ in ███ █████████, the ████████ ██████████ is the ███████████ ████ of the ███████ ██████████ ███████, in ███ █████████.

███████ █████████ and ██████████ ███████████ █████████

The ████████ █ ████ ███████ as a ████████ ████████ █████████ in the ███████ █████████. This is the ████████ █████████ that █████ a ███████-██████ ██████████ ████████ █ on the ████ ████ to the ████████ ███████ as:

$${\displaystyle \widehat{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}){\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

████████ there are ███████ █████████ ███████████ for the ███████ █████████ and ███ ███████, ███ ████ ██████████ ████ ███████ █ █████████. The above is the ████ █████████ ██████████, ███████, ██████ the ██████ ███████ ████████ on █^█ that is ████ an ███████ ████████████ of █^█ to █^∞.

The ██████████ ███████████ █████████ ████ ████████ the ██████ █. The ███████████ █████████ █████ a █████ █████ █████ on the ██████ to which it is ████████ to ████████ a ████████ ████ in █████ and in █████████: with ███ ███████████ for the ███████ █████████,

The ████████ ███████████, about the ███████████ in ████████████ ████████ and ████████ ████████████ of a ███████ ██████████ ██████, is █████████ below. The ██████████ of █ in the ████████ of ███████ ████████ is ██████████ a ███████████ of the █████–███ ███████ ███████, █████████ the ██████████ of the ███████████ ██████████████ of the ██████████ █████.

████████ █████████

The ██████ of ███████████ and ██████████ ██████████ use the ██████ ████████████ as a ██████ █████ for ███████ █████████; for ███████, ██████████ █████████ ██████ that the █████████████ █████ in ███████████ ███████ a ██████ ████████████. The ████████ ████████, which is the ███████████ ███████ ████████ of the ██████ ████████████ with ████ █ and ████████ █████████ █, █████████ ████████ █:

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}.}$$

The ██████ of ${\displaystyle \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}$ █████ the ████ under the █████ of █ █████ to ███, as is ████████ for a ███████████ ████████████. This ███████ from a ██████ of █████████ in the ████████ ████████:

$${\displaystyle {\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$$

which ████ that the ████ under the █████ ████ █████ in the ██████ is █████ to the ██████ ████ of █.

The ███████ █████ ███████ ████████ the ███████ ████ of ██████ █████████████, and ████ of █, in ███████████ and ██████████. This ███████ is ██████████ █████████ with the ████████ ████████████████ of █ as the ██████████ ██████████ with the ██████████ ███████████ █████████, and the ████ that ████████ █████ in the ███████████ █████████ ████ for the ████████ ████████. ████████████, █ is the ██████ ████████ ██████ the ████████ ██████ ████████████ █^−███ █████ to ███ ███ ███████ █████████. ██████, █████████ to ████ (████), the "█████ ████████" of ████████████ the ███████████ ████████ of ███████ ████████ ███████ to the ████████ ████████.

████████

The ████████ █ ███████ in the █████–██████ ███████ which ███████ the ████████████ ████████ of ████████ to █████ ████████. ████████████, if a ███████ ███████ █ has █████ █████████ █, ████

$${\displaystyle {\int }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}),}$$

█████ █(█) is the █████ ██████████████, which is an ███████. An ███████ is the ███████ ████ of a ██████ █ of █████████ █ (██ that ███ ██████ of █████████, which █████████ with ███ ██████, is ████ █.) The █████ ██████████████ of a ██████ can be ████████ from ███ ████████ ██████ and is █████ to be █████ to ███. ████ ██ have

$${\displaystyle A(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})={\int }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$

███████████ the ███████ for the ███████ ████ of a ██████ of ██████ █.

The ████████ ███████ in ████ █████ ████████ ████████ in ████████, in ██████████, █████ █████████ ██████████████ ███████ via the █████–████ ████████████.

██████'s ████████ ███████

███ of the ███ █████ in ███████ ████████ is ███████ ███████████ of a ████████ over a ██████████ ████████ (███████████) ██████ █████ █. A ████ of ██████'s ████████ ███████ ██████ that if a █████ █_█ is ████████ to █, ████

$${\displaystyle {\oint }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

████████ the █████ █ is not a ██████, and █████ ████ not have ███ ███████ ██████████ to the ████████ █, a ████████ █████ of this ██████ uses ██████'s ███████, which ███████ that the ████████ is █████████ under ████████ of the █████, ██ that it can be ████████ to a ██████ and ████ ██████████ ██████████ in █████ ███████████. ████ █████████, it is ████ that if a ███████████ ██████ █████ █ ████ not ███████ █_█, ████ the above ████████ is ███ █████ the ███████ ██████ of the █████.

The ███████ ████ of ██████'s ████████ ███████ ███████████ the ████████████ between the ██████ of a ███████ ████████ ████████ █(█) on the ██████ █████ █ and the █████ of █(█) at ███ ████████ █████ █_█ of █:

$${\displaystyle {\oint }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}),}$$

████████ █(█) is ████████ in the ██████ ████████ by █ and ███████ ████████████ to █. ██████'s ████████ ███████ is a ███████ ████ of the ███████ ███████, that if █(█) is a ███████████ ████████ on the ██████ ████████ by █ and is ██████████ in a █████████████ of █, ████

$${\displaystyle {\oint }_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\sum \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},a_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}),}$$

█████ the ███ is of the ████████ at the █████ of █(█).

██████ ████████ and ███████

The ████████ █ is ██████████ in ██████ ████████ and █████████ ██████, for ███████ in ███████'s ███, █████'s ███, ███████'s █████████, and ████ the ████████ █████ █████████. ███████ the ████████ ███████ of this is the ███-███████████ █████████ █████████, ████████████ the █████████ of a █████ ██████ at the ██████, █████ ██████████ █████ has ████ ███████ ████ through ███ ██████ and ████████ ██████ ███████ █████████ the ██████:

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>})=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}|\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}|.}$$

The ██████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ is █████████ to ██████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ███████████ ████████ of the ███████ ████████ in ${\displaystyle {\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$:

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},}$$

█████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the █████ █████ ████████.

In ██████ ██████████, ███████ of █ are ███████ because of a █████████████ by the █-███████████ ██████ of the ████ █-██████. For ███████, in █████ ██████████, the █████████ █████████ is:

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>})=-\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}|\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}|},}$$

which has the █-███████████ ██████ (█.█., the ████) of the ████ █-██████ in the ███████████.

█████ █████████

In the ████████████ ████████ of ██████, the █████ █████████ of a ██████ █████ █████ is the ██████ it █████ █████████████, in ███████, from █████ to ██████, ████████ as the ████████ of ██████ █████████ with ███████ to ███ ██████:

$${\displaystyle {\int }_a^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$$

For a ██████ █████, this ████████ is █████ to ███ for an ███████ █ ██████ the ███████ ██████ or █████ of the █████. █ is the ███████ ██████ about the ██████ of the █████████ of the █████ ████████████ by █████████, a ███ █████ █████ on the ████ ██████, █████████ by the ██████████ ███████ ██████ at ████ █████ on the ████████ █████. ████████████, █ is the ██████ of the ███ ██████ ████ █████ on the █████ to the █████████████ █████ on the █████████, █████████ to the █████ ███ for ████████.

█████ ████████ and ████████'s █████████████

The █████████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}!}$ is the ███████ of ███ of the ████████ ████████ through █. The █████ ████████ ███████ the ███████ of █████████ (████████ ███████ ████ for ███-████████ ████████) to ███ ███████ ███████, except the ████████ ████ ████████, with the ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})!}$. ████ the █████ ████████ is █████████ at ████-████████, the ██████ is █████████ █████████ in █████ of █. For ███████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})=\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and $\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sqrt{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

The █████ ████████ is ███████ by ███ ███████████ ███████ ███████████:

$${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\prod _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{\infty }}\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$$

█████ █ is the █████–██████████ ████████. █████████ at ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠ and ███████, the ████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}){\phantom{)}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ ███████ to the ██████ ███████ ███████. The █████ ████████ is ████ █████████ to the ███████ ████ ████████ and ██████████ for the ██████████ ███████████, in which the ████████ █ █████ an █████████ ████.

The █████ ████████ is used to █████████ the ██████ █_█(█) of the █-███████████ ████ of ██████ █ in █████████ █-███████████ █████, and the ███████ ████ █_█−█(█) of ███ ████████, the (█−█)-███████████ ██████:

$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\frac{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},}$$