On asymptotic expansions for basic hypergeometric functions

TL;DR

This paper develops new methods to derive asymptotic expansions for basic hypergeometric functions and related $q$-series, advancing understanding of their behavior at limits.

Contribution

Introduces a novel approach using Ono and Lovejoy's result to obtain asymptotic expansions for hypergeometric series and partial theta functions.

Findings

New asymptotic expansion techniques for $q$-series

Extensions to multi hypergeometric series

Improved understanding of asymptotic behavior

Abstract

This paper establishes new results concerning asymptotic expansions of $q$-series related to partial theta functions. We first establish a new method to obtain asymptotic expansions using a result of Ono and Lovejoy, and then build on these observations to obtain asymptotic expansions for related multi hypergeometric series.