DLMF:18.28.E10 (Q5985)

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Language	Label	Description	Also known as
English	DLMF:18.28.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\sum_{y=0}^{\infty}\frac{(1-q^{2y}a^{-2})\left(a^{% -2},(ab)^{-1};q\right)_{y}}{(1-a^{-2})\left(q,bqa^{-1};q\right)_{y}}(ba^{-1})^% {y}q^{y^{2}}\*Q_{n}\left(\tfrac{1}{2}(aq^{-y}+a^{-1}q^{y});a,b\,|\,q^{-1}% \right)\*Q_{m}\left(\tfrac{1}{2}(aq^{-y}+a^{-1}q^{y});a,b\,|\,q^{-1}\right)=% \frac{\left(qa^{-2};q\right)_{\infty}}{\left(ba^{-1}q;q\right)_{\infty}}\left(% q,(ab)^{-1};q\right)_{n}(ab)^{n}q^{-n^{2}}\delta_{n,m}.}}

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DLMF:18.28.E10

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Defining formula

{\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}

introduction.Sx4.p1.t1.r4.m5acdec

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Defining formula

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

C17.S2.SS1.p1.m2agdec

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$$q^{-1}$$ -Al-Salam–Chihara polynomial

Defining formula

{\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b}\,|\,% \NVar{q}^{-1}\right)}}

C18.S28.E9.m2aadec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

C17.S2.SS1.p1.m6aedec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1adec

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