A contiguous extension of Dixon’s theorem for a terminating 4F3(1) series with applications

Abstract

We derive a summation formula for the terminating hypergeometric series 4F3 [ −m, a, b, 1 + c 1 + a + m, 1 + a − b, c ; 1] , where m denotes a nonnegative integer. Using this summation formula, we establish a reduction formula for the Srivastava–Daoust double hypergeometric function with arguments z and −z . Special cases of this reduction formula lead to several reduction formulas for the hypergeometric functions p+1Fp with quadratic arguments when p = 2, 3 and 4 by employing series rearrangement techniques. A general double series identity involving a bounded sequence of arbitrary complex numbers is also given.