EXPONENTIALLY-IMPROVED ASYMPTOTICS FOR THE GAMMA FUNCTION

被引：21

作者：

PARIS, RB

WOOD, AD

机构：

[1] DUNDEE INST TECHNOL,DEPT MATH & COMP SCI,DUNDEE DD1 1HG,SCOTLAND

[2] DUBLIN CITY UNIV,SCH MATH SCI,DUBLIN 9,IRELAND

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1992年 / 41卷 / 1-2期

关键词：

EXPONENTIALLY-IMPROVED ASYMPTOTICS; GAMMA FUNCTION; MELLIN-BARNES INTEGRALS; STOKES MULTIPLIERS;

D O I：

10.1016/0377-0427(92)90243-Q

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By expressing the error term in truncation of the asymptotic expansion in terms of a Mellin-Barnes integral, we obtain an exponentially-improved asymptotic expansion for GAMMA(z) as absolute value of z --> infinity in \arg z\ < pi. We describe the need for such an expansion arising in applications. The result is compared with formal results of Dingle obtained via Borel summation and rigorous methods of Olver using Laplace integrals for a different class of functions.

引用

页码：135 / 143

页数：9

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