# Some $q$-series identities extending work of Andrews, Crippa, and Simon on sums of divisors functions

## TL;DR

This paper extends a theorem on the asymptotic behavior of $q$-series polynomials by incorporating exponential or periodic functions of the recursive index, broadening the scope of previous divisor sum identities.

## Contribution

It introduces a generalized recursive framework for $q$-series polynomials, extending prior results to include exponential and periodic functions of the recursion index.

## Key findings

- Generalized asymptotic formulas for $q$-series polynomials
- Extension of divisor sum identities to new recursive classes
- Broadened understanding of recursive polynomial behavior in $q$-series

## Abstract

In this article we extend a theorem of Andrews, Crippa, and Simon on the asymptotic behavior of polynomials defined by a general class of recursive equations. Here the polynomials are in the variable $q$, and the recursive definition at step $n$ introduces a polynomial in $n$. Our extension replaces the polynomial in $n$ with either an exponential or periodic function of $n$.