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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

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Correction terms in the asymptotic expansion of hypergeometric function

I am interested in obtaining the asymptotic expansion of $r(\rho)$ (which is the inverse of $\rho$ below), $$\rho=\frac{2b}{1-q}\left(1-\left(\frac br\right)^{1-q}\right)^{1/2}\left(_2F_1\left(\frac{1 …
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