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Asymptotic behavior of functions, asymptotic series and related topics

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Hypergeometric function asymptotics

I came across the following hypergeometric function recently: $$ _2F_1(1-n,p-2n+1;p-n+1;x) $$ where $p > 0$ is a non-integer constant, $n$ some large positive integer, and $x > 0$ a small constant. …