Hankel determinants of backward shifts of the coefficients of a partial theta function

TL;DR

This paper investigates polynomials connected to Hankel determinants derived from backward shifts of partial theta function coefficients, providing new formulas for the reciprocal's coefficients.

Contribution

It introduces a novel study of polynomials related to Hankel determinants of partial theta function coefficients and derives a simple formula for the reciprocal's coefficients.

Findings

Polynomials related to Hankel determinants are characterized.

A simple formula for the reciprocal's coefficients is established.

The study enhances understanding of the structure of partial theta functions.

Abstract

We study some polynomials which are related to Hankel determinants of backward shifts of the coefficients of a partial theta function. In this version an appendix is added which gives a simple formula for the coefficients of the reciprocal of the partial theta function.