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Asymptotic behavior of functions, asymptotic series and related topics
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Accepted
Asymptotic form of the Gauß Hypergeometric function 2F1 for three parameters approaching inf...
In fact your function is elementary and very simple, for its explicit form look at Brychkov,Marichev,Prudnikov, Integral and Series, vol.3 :
$$
F(a,a+1/2;2a;z)=\frac{1}{\sqrt{1-z}}\left(\frac{2}{1+\sq …