SOME REDUCTION FORMULAS FOR THE FUNCTIONS OF GAUSS AND CLAUSEN

摘要

The aim of this article is to obtain the closed forms of five reduction formulas (believed to be new) for Gauss functions _2F_1[α, α ± 1/2; 2α ? 1; z], _2F_1[α ? 1, α ? 3/2; 2α ? 1; z] and Clausen function _3_F_2[γ+1, β, β - 1/2; γ, 2β; z], using series rearrangement technique. As application of our closed forms of two reduction formulas, we establish four results for the reducibility of general Srivastava-Daoust double hypergeometric function in terms of generalized hypergeometric functions of one variable, with suitable convergence conditions.