The q-binomial formula and the Rogers dilogarithm identity

TL;DR

This paper demonstrates that the q-binomial formula, as q approaches 1, is equivalent to the Rogers five-term dilogarithm identity, linking combinatorial identities with special functions.

Contribution

It establishes a novel equivalence between the q-binomial formula and the Rogers dilogarithm identity in the limit q→1.

Findings

q-binomial formula converges to Rogers dilogarithm identity as q approaches 1

Provides a new perspective connecting combinatorics and special functions

Highlights the limit behavior linking q-series to classical identities

Abstract

The q-binomial formula in the limit q->1 is shown to be equivalent to the Rogers five term dilogarithm identity.