A Comprehensive Study of Complete Generalized New Mock Theta Functions

TL;DR

This paper generalizes new mock theta functions, providing their bilateral forms, series expansions via Slater's transformation, and continued fraction representations, advancing the mathematical understanding of these special functions.

Contribution

It introduces a comprehensive generalization of new mock theta functions, including bilateral forms, series expansions, and continued fractions, which were not previously explored together.

Findings

Derived bilateral generalized new mock theta functions.

Expressed these functions as 2 phi 1 series using Slater's transformation.

Provided continued fraction representations of the generalized functions.

Abstract

The generalization of new mock theta functions of Andrews and Bringmann et al are given. Further we have given the expansion of these bilateral generalized new mock theta functions as 2 phi 1 series by Slaters transformation. After that we have given the continued fraction representation of these generalized mock theta functions.