Formula:6671

Digital Library of Mathematical Functions ID 18.27.E24

${\displaystyle{\displaystyle\sum_{\ell=-\infty}^{\infty}\left(\tilde{h}_{n}\left(cq^{\ell};q\right)\tilde{h}_{m}\left(cq^{\ell};q\right)+\tilde{h}_{n}\left(-cq^{\ell};q\right)\tilde{h}_{m}\left(-cq^{\ell};q\right)\right)\frac{q^{\ell}}{\left(-c^{2}q^{2\ell};q^{2}\right)_{\infty}}=2\frac{\left(q^{2},-c^{2}q,-c^{-2}q;q^{2}\right)_{\infty}}{\left(q,-c^{2},-c^{-2}q^{2};q^{2}\right)_{\infty}}\frac{\left(q;q\right)_{n}}{q^{n^{2}}}\delta_{n,m},}}$

Constraint(s)

${\displaystyle{\displaystyle c>0}}$

Symbols List

• ${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$:
• ${\displaystyle{\displaystyle\tilde{h}_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)}}$: discrete $$q$$ -Hermite II polynomial
• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: real variable
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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