International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 547459, 14 pages
http://dx.doi.org/10.1155/2012/547459
Research Article

The Multiple Gamma-Functions and the Log-Gamma Integrals

X.-H. Wang1 and Y.-L. Lu2

1Xi’an International Studies University, Xi’an, Shaanxi 710128, China
2Department Of Mathematics, Weinan Teachers’ College, Shaanxi 714000, China

Received 15 May 2012; Accepted 30 July 2012

Academic Editor: Shigeru Kanemitsu

Copyright © 2012 X.-H. Wang and Y.-L. Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, which is a companion paper to [W], starting from the Euler integral which appears in a generalization of Jensen’s formula, we shall give a closed form for the integral of log . This enables us to locate the genesis of two new functions and considered by Srivastava and Choi. We consider the closely related function A(a) and the Hurwitz zeta function, which render the task easier than working with the functions themselves. We shall also give a direct proof of Theorem 4.1, which is a consequence of [CKK, Corollary 1.1], though.