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arXiv · 1609.08743

Inequalities for Zero-Balanced Gaussian hypergeometric function

Ti-Ren Huang·Xiao-Yan Ma·Xiao-Hui Zhang
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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 $δ\in(a-1,0)$, and study the problem of comparing these two functions, thus get the largest value $δ_1=δ_1(a,c,d)$ such that the inequality $F(a-1,b;a+b;1-x^c)<F(a-1-δ,b+δ;a+b;1-x^d)$ holds for all $x\in (0,1)$.

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Ti-Ren Huang, Xiao-Yan Ma, Xiao-Hui Zhang. 2016-09-28. Inequalities for Zero-Balanced Gaussian hypergeometric function. https://arxiv.org/abs/1609.08743

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