████ ████████████

████-██████ ████ █████████

The above can be ████████████ in ███ █████████ by ████████ the ███████ for the ███ of ███ █████. The ████████ for the █████████ of a ██████████ ████ █████████ to the █████ along the █-████ is $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=A\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$$ █████ ${\displaystyle A}$ is the ████ █████████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ██████████ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ███████ █████████ of the ████. ███████ a ██████ ████ of the ████ █████████ and █████████ but with a █████████ █████ is ████ █████████ to the █████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=A\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$$ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the █████ ██████████ between the █████ in ███████. The ███ █████ will █████████ and ███: the ███ of the ███ █████ is $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=A[\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})].}$$ Using the █████████████ ████████ for the ███ of ███ ███████: $\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}a+\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\left(\frac{a-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right)\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\left(\frac{a+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right),$ this can be ███████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\left(\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right)\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\left(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right).}$$ This ██████████ a ████ at the ████████ █████████, █████████ to the █████ like ███ ██████████, █████ █████████ is ████████████ to the ██████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

• ████████████ ████████████: If the █████ ██████████ is an ████ ████████ of █: ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\dots ,-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\dots }$ ████ ${\displaystyle \left|\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\right|=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ██ the ███ of the ███ █████ is a ████ with █████ the █████████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}A\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$$
• ███████████ ████████████: If the █████ ██████████ is an ███ ████████ of █: ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\dots ,-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\dots }$ ████ ${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ██ the ███ of the ███ █████ is ████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}+{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$$

Between ███ █████ █████

A ██████ ████ of ████████████ ███████ is ████████ if ███ █████ █████ of the ████ █████████ █████████ at an █████. ███ ████ is ██████████ ████████████, and the █████ is ██████████ █████████ at an █████ █ to the █████ ████. ████████ that the ███ █████ are in █████ at the █████ █, ████ the ████████ █████ ███████ along the █-████. The █████ ██████████ at the █████ A is █████ by

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

It can be ████ that the ███ █████ are in █████ ████

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

and are ████ a █████ out of █████ ████

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

████████████ ████████████ ██████ ████ the █████ are in █████, and ███████████ ████████████ ████ they are ████ a █████ out of █████. ████, an ████████████ ██████ ███████ is ████████, █████ the ██████████ of the ██████ is

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

and █_█ is █████ as the ██████ ███████. The ██████ ███████ █████████ with ████████ in ██████████, and with ██████████ █████ █.

The ███████ are ████████ ████████ the ███ █████ ███████ and the ██████ ███████ is ███████ ██████████.

Between ███ █████████ █████

A █████ ██████ ████████ a █████████ ████. If the █████ from ███ █████ ███████ ████████, the ████████████ ███████ ████ out the ███ in which the █████ ██████████ between the ███ █████ ██████ in █████. This ███████ on the ██████████ and on the ██████████ of the █████ ███████. The ██████ to the █████ █████ ████████████ between ███ █████████ █████. The ██████████ █████████ from ███ to ██████, and the ████████ between the ███████ █████████ from ████ to █████.

████ the █████ of ███████████ is ███ ██████ ████, the ██████ ███████ will be a ██████ of ██████ ████████ █████, since the █████ will ████ be ██████ ██████.

████████ █████

████████████ ██████ ████ ███████ █████ are █████ ████████ ████████ that the █████ ███████████ between ████ ██████ ████████ over the ███████████ ████.

It is █████████ █████████ for ███████ █████ of the ████ █████████ and █████████ to ███ to ████ (that is, █████████ █████████████, ██████). This is the █████████ behind, for ███████, █-█████ █████ and the ███████████ ███████. In ████ of █████ █████, the ██████ is ████████ by ███████ ███████ of the ██████.

It is ████ to ███ that a ███ of █████ will ██████ if they have the ████ █████████ and █████ ██████ are ██████ ███████ in █████. Using ███████, ████ ████ can be ███████████ as ${\displaystyle A{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}$ for ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ from ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, █████ $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}-{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

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

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

The █████–█████ ██████████████ uses ████████████ between ████████ ███████████.

A ███████████ ███████ can be ██████████ to be a ████████-████ ██████████████; since the █████ which it ████████ are █████████ by ████████████ between the █████ ███████████ by ████ of the ████████ in the ███████; ███ ████████████ ██. ███████████ for ███████ ██████████.