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Zbl 0983.41020
Ferreira, Chelo; López, José L.
An asymptotic expansion of the double gamma function. (English)
[J] J. Approximation Theory 111, No.2, 298-314 (2001). ISSN 0021-9045

The Barnes double gamma function $G(z)$ satisfies the recursion $G(z+1)=\Gamma(z)G(z)$. This paper gives a new integral representation for $\log G(z)$ and an asymptotic expansion for this function in negative powers of $z$ for large complex $z$ ($z$ not negative real). An error bound for the remainder at any order is supplied, and numerical experiments show the accuracy of the expansion and of the bounds.
[N.M.Temme (Amsterdam)]

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

Keywords: double gamma function; asymptotic expansion

Cited in: Zbl 1129.33001 Zbl 1061.41023

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