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arXiv · 1104.4736

On quotients and differences of hypergeometric functions

Slavko Simić·Matti Vuorinen
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Abstract

For Gaussian hypergeometric functions $F(x)= F(a,b;c;x),$ $a,b,c>0,$ we consider the quotient $ Q_F(x,y)= (F(x)+F(y))/F(z)$ and the difference $ D_F(x,y)= F(x)+F(y)-F(z)$ for $0<x,y<1$ with $z=x+y-xy \,.$ We give best possible bounds for both expressions under various hypotheses about the parameter triple $(a,b;c)\,.$

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Slavko Simić, Matti Vuorinen. 2011-04-25. On quotients and differences of hypergeometric functions. https://arxiv.org/abs/1104.4736

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