Generalization of a summation formula due to Fox - Medhat A. Rakha (Journal of the Egyptian Mathematical Society, 2013)
By employing classical Gauss’s second summation theorem for the series 2F1, Fox established the following interesting and useful summation formula for the series 3F212 viz. 3F2α,β,γ;12α-m,12(β+γ+1);=Γ(α-m)Γ12β+12γ+12Γ(β)Γ(γ)2β+γ-2π∑r=0mmrΓ12β+12rΓ12γ+12r2rΓ(r+α-m) where m is a positive integer. The aim of this research paper is to provide the generalization of Fox’s summation formula and to obtain 19 results of this type. The results are derived with the help of generalized Gauss’s second summation theorem recently obtained by Rakha, et al. and a general formula due to Fox. The results derived in this paper are simple, interesting, easily established and may be potentially useful.