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

Asymptotic expansions of the Gauss hypergeometric function with large parameters, {equation presented}, are known for many special cases, but not for one that the author encountered in recent work on fluid mechanics: ϵ2 = 0 and.ϵ3=ϵ1z. This paper gives the leading term for that case if β is not a negative integer and z is not on the branch cut [1, ∞), and it shows how subsequent terms can be found. © Australian Mathematical Society 2019. This is the author's version of the article. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. The Version of Record was published in The ANZIAM Journal https://doi.org/10.1017/S1446181119000166.