Formula:6158

Digital Library of Mathematical Functions ID 17.12.E4

${\displaystyle{\displaystyle\sum_{n=0}^{\infty}q^{n^{2}}a^{n}\beta_{n}=\frac{1}{\left(aq;q\right)_{\infty}}\sum_{n=0}^{\infty}q^{n^{2}}a^{n}\alpha_{n}.}}$

Symbols List

• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\alpha_{n}}}$: part of Bailey pair
• ${\displaystyle{\displaystyle\beta_{n}}}$: part of Bailey pair
 

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