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

Authors

DOI:

https://doi.org/10.21914/anziamj.v62.14210

Keywords:

asymptotic expansion, hypergeometric functions, large parameters

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

Author Biography

John Harper, Victoria University of Wellington, New Zealand

Emeritus professor, School of Mathematics and Statistics, 

Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand

Published

2021-04-25

Issue

Section

Special Issue for Renown Researcher