Abstract
By the different modification of J_<2a+2n-k>(x) Σ^∞_<i=0>Γ(2b-2a+i)/(i!Γ(2b-2a)). J_<-2a-2n+2i>(x), we obtain an identity A(a, b, n, k, l) ≡ B(a, b, n, k, l), where A(a, b, n, k, l) and B(a, b, n, k, l) are given in the paper. Rewriting A(a, b, n, k, l) and B(a, b, n, k, l) with Pochhammer's symbol, setting l = n, substituting 2n to k and using the relation (0)_0 = 1, (0)_i = 0 (i ≥ 1), we have discovered the following summation formula of the finite generalized hypergeometric series, [numerical formula], When n (≥ 0) is an integer. Similarly, setting l = n, substituting 2n + 1 to k, we have also obtained the following formula [numerical formula].
