A Bailey type identity with applications related to integer representations

El Bachraoui, Mohamed

doi:10.1090/proc/15407

A Bailey type identity with applications related to integer representations
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by Mohamed El Bachraoui PDF

Proc. Amer. Math. Soc. 149 (2021), 3187-3200 Request permission

Abstract:

In this paper we shall deduce a Bailey type formula as a consequence of the residual identity of a $q$-series transformation due to Gasper. Our formula leads to a variety of $q$-series identities which are related to the arithmetic function counting integer representations of the form \[ \frac {n(An+B)}{2}+\frac {r(Cr+D)}{2} + Enr. \]

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