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Zbl 0848.33001
Olver, F.W.J.
On an asymptotic expansion of a ratio of gamma functions. (English)
[J] Proc. R. Ir. Acad., Sect. A 95, No.1, 5-9 (1995). ISSN 0035-8975

The expansion reads $$\Gamma (n+ a) \Gamma (n+b)/ \Gamma (n+1) \sim \sum^\infty_{s=0} (-1)^s (1-a)_s (1-b)_s \Gamma (n+a+ b-s- 1)/s!, \quad \text{as }n\to \infty,$$ $|\arg n|\leq \pi- \varepsilon$, in which $(p)_s= \Gamma (p+ s)/ \Gamma (p)$. The method of proof is based on a contour integral and furnishes an integral representation of the remainder in the expansion.
[N.M.Temme (Amsterdam)]

MSC 2000:: *33B15 Gamma-functions, etc.
41A60 Asymptotic problems in approximation

Keywords: gamma function; asymptotic expansion

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