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arXiv · 2004.01945

Uniform asymptotics of a Gauss hypergeometric function with two large parameters, V

R. B. Paris
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Abstract

We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+\epsilon\lambda,b;c+\lambda;x),\qquad 0 1$ and the constants $a$, $b$ and $c$ are supposed finite. Use of a standard integral representation shows that the problem reduces to consideration of a simple saddle point near an endpoint of the integration path. A uniform asymptotic expansion is first obtained by employing Bleistein's method. An alternative form of uniform expansion is derived following the approach described in Olver's book [{\it Asymptotics and Special Functions}, p.~346]. This second form has several advantages over the Bleistein form.

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R. B. Paris. 2020-04-04. Uniform asymptotics of a Gauss hypergeometric function with two large parameters, V. https://arxiv.org/abs/2004.01945

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