The multiple gamma function and its application to computation of series

被引：38

作者：

Adamchik, VS ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Dept Comp Sci, Pittsburgh, PA 15213 USA

来源：

RAMANUJAN JOURNAL | 2005年 / 9卷 / 03期

关键词：

multiple gamma function; Barnes function; gamma function; Riemann zeta function; Hurwitz zeta function; Stirling numbers; Stieltjes constants; Catalan's constant; harmonic numbers; Glaisher's constant;

D O I：

10.1007/s11139-005-1868-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The multiple gamma function Gamma(n), defined by a recurrence-functional equation as a generalization of the Euler gamma function, was originally introduced by Kinkelin, Glaisher, and Barnes around 1900. Today, due to the pioneer work of Conrey, Katz and Sarnak, interest in the multiple gamma function has been revived. This paper discusses some theoretical aspects of the Gamma(n) function and their applications to summation of series and infinite products.

引用

页码：271 / 288

页数：18

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