Generalized Watson's summation formula for 3F2(1)

[摘要] A summation formula is given for F-3(2)(a, b, c; 1/2(a + b + i + 1), 2c + j; 1) with fixed j and arbitrary i (i, j is an element of Z). This result generalizes the classical Watson's theorem which deals with the case i = j = 0. Extensions to the cases of F-3(2)(a, 1 + i + j - a, c; e, 1 + i + 2c - e; 1), and F-3(2)(a, b, c; 1 + i + a - b, 1 + i + j + a - c; 1) are given. Notice that the case i = j = 0 corresponds to the classical theorems due to Whipple and Dixon, respectively.

[发布日期] 1997-12-10

[关键词] generalized hypergeometric functions;Watson's summation theorem