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