Bailey-type factorizations for Horn functions

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 $H_5$.