Inequalities for Zero-Balanced Gaussian hypergeometric function

2016/09/28 by Huang, Ti-Ren, Ma, Xiao-Yan, Zhang, Xiao-Hui
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.08743

Abstract

In this paper, we consider the monotonicity of certain combinations of the Gaussian hypergeometric functions F(a-1,b;a+b;1-x^c) and F(a-1-δ,b+δ;a+b;1-x^d) on (0,1) for δ∈(a-1,0), and study the problem of comparing these two functions, thus get the largest value δ₁=δ₁(a,c,d) such that the inequality F(a-1,b;a+b;1-x^c)

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