Some [formula omitted]-series identities extending work of Andrews, Crippa, and Simon on sums of divisors functions

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.