DLMF:18.35.E4 (Q6043): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:18.35.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P^{(\lambda)}_{n}\left(\cos\theta;a,b\right)=% \frac{{\left(\lambda-\mathrm{i}\tau_{a,b}(\theta)\right)_{n}}}{n!}e^{\mathrm{i% }n\theta}\*{{}_{2}F_{1}}\left({-n,\lambda+\mathrm{i}\tau_{a,b}(\theta)\atop-n-% \lambda+1+\mathrm{i}\tau_{a,b}(\theta)};e^{-2\mathrm{i}\theta}\right)=\sum_{% \ell=0}^{n}\frac{{\left(\lambda+\mathrm{i}\tau_{a,b}(\theta)\right)_{\ell}}}{% \ell!}\frac{{\left(\lambda-\mathrm{i}\tau_{a,b}(\theta)\right)_{n-\ell}}}{(n-% \ell)!}e^{\mathrm{i}(n-2\ell)\theta}.}}

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DLMF:18.35.E4

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Symbols defined

Pollaczek polynomial

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Defining formula

{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

C16.S2.m5adec

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