Bailey-type factorizations for Horn functions

TL;DR

This paper extends Bailey's classical identity to Horn's hypergeometric functions, providing new factorizations that decompose complex functions into simpler components, enhancing understanding of hypergeometric identities.

Contribution

The paper introduces Bailey-type factorizations for Horn's hypergeometric functions H_1, H_4, and H_5, expanding the scope of classical hypergeometric identities.

Findings

Bailey-type factorizations for H_1, H_4, and H_5 derived

Decomposition of Horn functions into products of simpler hypergeometric functions

Enhanced understanding of hypergeometric function identities

Abstract

In this paper we are interested in extending Bailey's identity to other classical hypergeometric functions. Bailey's identity states that under a suitable choice of parameters, Appell's $F_4$ decomposes into a product of two ${}_2F_1$'s. We will show how Bailey-type factorizations can be found for Horn's hypergeometric functions $H_1, H_4$ and $H_5$.