Formula:6669

Digital Library of Mathematical Functions ID 18.27.E22

${\displaystyle{\displaystyle\sum_{\ell=0}^{\infty}\left(h_{n}\left(q^{\ell};q\right)h_{m}\left(q^{\ell};q\right)+h_{n}\left(-q^{\ell};q\right)h_{m}\left(-q^{\ell};q\right)\right)\*\left(q^{\ell+1},-q^{\ell+1};q\right)_{\infty}q^{\ell}=\left(q;q\right)_{n}\left({q,-1,-q};q\right)_{\infty}q^{n(n-1)/2}\delta_{n,m}.}}$

Symbols List

• ${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$:
• ${\displaystyle{\displaystyle h_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)}}$: discrete $$q$$ -Hermite I 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
 

Resources that cite this formula

No records found.