The Ramanujan Journal

, Volume 9, Issue 3, pp 271–288

The Multiple Gamma Function and Its Application to Computation of Series

Authors

    • Department of Computer ScienceCarnegie Mellon University
Article

DOI: 10.1007/s11139-005-1868-3

Cite this article as:
Adamchik, V.S. Ramanujan J (2005) 9: 271. doi:10.1007/s11139-005-1868-3

Abstract

The multiple gamma function Γn, 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 Γn function and their applications to summation of series and infinite products.

Keywords

multiple gamma functionBarnes functiongamma functionRiemann zeta functionHurwitz zeta functionStirling numbersStieltjes constantsCatalan’s constantharmonic numbersGlaisher’s constant

Copyright information

© Springer Science + Business Media, Inc. 2005