Certain results on Wright's generalized hypergeometric functions with applications (Q2710532)

The authors study the integral \(I=\int^1_{-1}(1-x)^a(1+x)^b f({1 \over 2}(1-x))dx\), where \(f\) is a gamma fraction multiplied by a Wright hypergeometric function \(_{p+2}\psi_{q+2}\) with certain conditions on some of the parameters. Using term-by-term integration, they establish an expression of \(I\) in terms of \(_{q+4}\Psi_{q+3}\). Moreover, the partial derivatives \(\partial I/ \partial a\) and \(\partial I/ \partial b\) are found; these expressions include series involving the digamma function. A number of special cases are considered as well as some formulas obtained by comparison with known summation theorems.