New double-sum expansions for certain Mock theta functions

Abstract

The study of expansions of certain mock theta functions in special functions theory has a long and quite significant history. Motivated by recent correlations between q-series and mock theta functions, we establish a new q-series transformation formula and derive the double-sum expansions for mock theta functions. As an application, we state new double-sum representations for certain mock theta functions.

Keywords

• basic hypergeometric series
• mock theta functions
• double sums