Some elementary remarks on the powers of a partial theta function and corresponding q-analogs of the binomial coefficients

TL;DR

This paper derives formulas for the coefficients of both positive and negative powers of a partial theta function, enhancing understanding of its structure and related q-analogs of binomial coefficients.

Contribution

It provides new explicit formulas for the coefficients of partial theta functions and their q-analogs, expanding theoretical knowledge in this area.

Findings

Formulas for coefficients of positive powers

Formulas for coefficients of negative powers

Connections to q-analogs of binomial coefficients

Abstract

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.