An elementary proof of a certain transformation for an \(n\)-balanced hypergeometric \({}_ 3\Phi _ 2\) series (Q1098978)

The authors give an interesting generalization of a theorem of \textit{H. M. Srivastava} [Proc. Am. Math. Soc. 101, 108--112 (1987; Zbl 0607.33005)], which asserts the symmetry in \(n\) and \(N\) of a function \(f(n,N)\) defined in terms of an \(n\)-balanced basic (or \(q\)-) hypergeometric \({}_ 3\Phi_ 2\) series. Their proof of this generalization is rather elementary; it is based only upon the familiar Heine transformation for \({}_ 2\Phi_ 1\).