Asymptotics of a Gauss hypergeometric function with two large parameters: a new case
DOI:
https://doi.org/10.21914/anziamj.v62.14210Keywords:
asymptotic expansion, hypergeometric functions, large parametersAbstract
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.
Published
2021-04-25
Issue
Section
Special Issue for Renown Researcher