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Asymptotics of a Gauss Hypergeometric Function With Two Large Parameters : A New Case
Asymptotic expansions of the Gauss hypergeometric function with large parameters,
F(α+ϵ1τ,β+ϵ2τ;γ+ϵ3τ;z) as|τ|→∞, 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.
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