On certain products of hypergeometric series (Q1115997)

Let \(y_ 1(x)=_ 2F_ 1(\alpha,\beta,\gamma,x)\), \(y_ 2(x)=x^{1- \gamma}_ 2F_ 1(\alpha +1-\gamma,\beta +1-\gamma,2-\gamma,x)\). The main result in the paper is an expression for the quantity \(y_ 1^{(i)}(x)y_ 2^{(j)}(x)-y_ 1^{(j)}(x)y_ 2^{(i)}(x)\) as a finite sum of terms involving power functions and \(_ 2F_ 1's\). By comparing coefficients of powers of x, the author derives a second theorem involving two terminating nearly-poised \(_ 4F_ 3(1)'s.\) \{Reviewer's remark: In the latter formula, a power of -1 seems to be missing.\}