On q-series identities with multiple sums related to divisor functions

TL;DR

This paper reviews and extends q-series identities involving multiple sums related to divisor functions, providing clearer explanations and more powerful formulations of these mathematical identities.

Contribution

It offers an exposition of existing q-identities with multiple sums and derives stronger versions of these identities.

Findings

Enhanced formulations of q-series identities

Deeper understanding of divisor function relations

Unified exposition of multiple sum identities

Abstract

We provide an exposition of q-identities with multiple sums related to divisor functions given by Dilcher, Prodinger, Fu and Lascoux, Zeng, Guo and Zhang. Meanwhile, for each of these identities, a more powerful statement will be derived through our exposition.