Formula:6681

Digital Library of Mathematical Functions ID 18.28.E10

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

Symbols List

• ${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$:
• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b}\,|\,\NVar{q}^{-1}\right)}}$: $$q^{-1}$$ -Al-Salam–Chihara polynomial
• ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle q}}$: real variable
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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