  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 $H_5$.
