Bailey-type factorizations for Horn functions

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 ${}_2{F}_1$'s. We will show how Bailey-type factorizations can be found for Horn's hypergeometric functions $H_1,H_4$ and $H_5$.

19 pages