DLMF:18.15.E1 (Q5691)

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Language	Label	Description	Also known as
English	DLMF:18.15.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left(\sin\tfrac{1}{2}\theta\right)^{\alpha+\frac{% 1}{2}}\left(\cos\tfrac{1}{2}\theta\right)^{\beta+\frac{1}{2}}P^{(\alpha,\beta)% }_{n}\left(\cos\theta\right)=\pi^{-1}2^{2n+\alpha+\beta+1}\mathrm{B}\left(n+% \alpha+1,n+\beta+1\right)\*\left(\sum_{m=0}^{M-1}\frac{f_{m}(\theta)}{2^{m}{% \left(2n+\alpha+\beta+2\right)_{m}}}+O\left(n^{-M}\right)\right),}}

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DLMF:18.15.E1

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}

C5.S12.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}

C18.S3.T1.t1.r2.m2adec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2adec

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