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arXiv · 1408.5268

The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants

R. B. Paris
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Abstract

We obtain convergent inverse factorial expansions for the sum $S_n(a,b;c)$ of the first $n$ terms of the Gauss hypergeometric function of unit argument valid for $n\geq 1$. The form of these expansions depends on the location of the parametric excess $s:=c-a-b$ in the complex $s$-plane. The leading behaviour as $n\rightarrow\infty$ agrees with previous results in the literature. The case $a=b=1/2$, $c=1$ corresponds to the Landau contants.

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R. B. Paris. 2014-08-22. The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants. https://arxiv.org/abs/1408.5268

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