On a new class of integrals involving generalized hypergeometric function ?F?

Abstract

The main aim of this research paper is to evaluate a general integral of the form Z 1 0 x d?1 (1 ? x) d+` [1 + ?x + ?(1 ? x)]?2d?`?1 × 4F3 a, b, 2d + ` + 1, c 1 2 (a + b + i + 1), d, 2c + j ; (1 + ?)x 1 + ?x + ?(1 ? x) dx in the most general form for any ` ? Z and i, j = 0, ±1, ±2. The results are established with the help of generalized Watson’s summation theorem due to Lavoie, et al. More than fifty interesting general integrals have also been obtained as special cases of our main findings.