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arXiv · 2008.01601

Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters

Nico M. Temme
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Abstract

We derive asymptotic expansions of the Kummer functions $M(a,b,z)$ and $U(a,b+1,z)$ for large positive values of $a$ and $b$, with $z$ fixed. For both functions we consider $b/a\le 1$ and $b/a\ge 1$, with special attention for the case $a\sim b$. We use a uniform method to handle all cases of these parameters.

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Nico M. Temme. 2020-08-04. Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters. https://arxiv.org/abs/2008.01601

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