Multiple Gamma Function and Its Application to Computation of Series

Details Multiple Gamma Function and Its Application to Computation of Series Multiple Gamma Function and Its Application to Computation of Series

2003-08-07

arxiv.org/abs/math/0308074v1

Mathematics

Classical Analysis and ODEs

20 pages, Latex, uses kluwer.cls, will appear in The Ramanujan Journal

Scientific paper

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.

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