Asymptotics of a Gauss hypergeometric function with two large parameters: a new case

Abstract

Asymptotic expansions of the Gauss hypergeometric function with large parameters, $F(\alpha+\epsilon_1\tau,\beta+\epsilon_2\tau;\gamma+\epsilon_3\tau;z)$ as $|\tau|\to\infty$, are known for many special cases, but not for one that the author encountered in recent work on fluid mechanics: $\epsilon_2=0$ and $\epsilon_3=\epsilon_1 z$. This paper gives the leading term for that case if  $\beta$ is not a negative integer and $z$ is not on the branch cut $[1,\infty)$, and it shows how subsequent terms can be found.

doi:10.1017/S1446181119000166