Rational hypergeometric identities

TL;DR

This paper explores a special limit of the Faddeev modular quantum dilogarithm, leading to new hypergeometric identities involving bilateral Mellin-Barnes integrals with Pochhammer symbols.

Contribution

It introduces a novel class of hypergeometric identities derived from a singular limit of the hyperbolic gamma function.

Findings

New hypergeometric identities involving bilateral Mellin-Barnes integrals

Connection between quantum dilogarithm limits and hypergeometric sums

Potential applications in mathematical physics and special functions

Abstract

A special singular limit $\omega_1/\omega_2\to 1$ is considered for the Faddeev modular quantum dilogarithm (hyperbolic gamma function) and the corresponding hyperbolic integrals. It brings a new class of hypergeometric identities associated with bilateral sums of Mellin-Barnes type integrals of particular Pochhammer symbol products.