DLMF:18.28.E7 (Q5982): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:18.28.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle Q_{n}\left(\cos\theta;a,b\,|\,q\right)=p_{n}\left% (\cos\theta;a,b,0,0\,|\,q\right)=a^{-n}\sum_{\ell=0}^{n}q^{\ell}\frac{\left(% abq^{\ell};q\right)_{n-\ell}\left(q^{-n};q\right)_{\ell}}{\left(q;q\right)_{% \ell}}\*\prod_{j=0}^{\ell-1}(1-2aq^{j}\cos\theta+a^{2}q^{2j})=\frac{\left(ab;q% \right)_{n}}{a^{n}}{{}_{3}\phi_{2}}\left({q^{-n},ae^{\mathrm{i}\theta},ae^{-% \mathrm{i}\theta}\atop ab,0};q,q\right)=\left(be^{-\mathrm{i}\theta};q\right)_% {n}e^{\mathrm{i}n\theta}{{}_{2}\phi_{1}}\left({q^{-n},ae^{\mathrm{i}\theta}% \atop b^{-1}q^{1-n}e^{\mathrm{i}\theta}};q,b^{-1}qe^{-\mathrm{i}\theta}\right)% .}}

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DLMF:18.28.E7

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Symbols defined

Al-Salam–Chihara polynomial

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Askey–Wilson polynomial

Defining formula

{\displaystyle{\displaystyle p_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c},\NVar{d}\,|\,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}

C18.S28.E1.m2aadec

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