An asymptotic expansion of the double gamma function

被引：42

作者：

Ferreira, C ^{[1
]}

López, JL

机构：

[1] Univ Zaragoza, Fac Ciencias, Dept Math Aplicada, E-50013 Zaragoza, Spain

[2] Univ Publ Navarra, Dept Matemat & Informat, Pamplona 31006, Spain

来源：

JOURNAL OF APPROXIMATION THEORY | 2001年 / 111卷 / 02期

关键词：

Barnes double gamma function; asymptotic expansions;

D O I：

10.1006/jath.2001.3578

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Barnes double gamma function G(z) is considered for large argument z. A new integral representation is obtained for log G(z). An asymptotic expansion in decreasing powers of : and uniformly valid for \ Arg z \ < pi is derived from this integral. The expansion is accompanied by an error bound at any order of the approximation. Numerical experiments show that this bound is very accurate for real z. The accuracy of the error bound decreases for increasing Arg z. (C) 2001 Academic Press.

引用

页码：298 / 314

页数：17

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