Vol. 8, No. 4, 2015

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A type of multiple integral with log-gamma function

Duokui Yan, Rongchang Liu and Geng-zhe Chang

Vol. 8 (2015), No. 4, 593–614
Abstract

In this paper, we give a general formula for the multiple integral

I =010101f(x 1 + x2 + + xn)dx1dx2dxn.

As an application, the integral I with f(x) = logΓ(x) is evaluated for all n . The subsidiary computational challenges are interesting in their own right.

Keywords
multiple integral, log-gamma function
Mathematical Subject Classification 2010
Primary: 05A19, 54C30
Milestones
Received: 21 April 2014
Revised: 27 July 2014
Accepted: 28 July 2014
Published: 23 June 2015

Communicated by Kenneth S. Berenhaut
Authors
Duokui Yan
School of Mathematics and System Science
Beihang University
Beijing 100091
China
Rongchang Liu
School of Mathematics and System Science
Beihang University
Beijing 100191
China
Geng-zhe Chang
School of Mathematical Science
University of Science and Technology of China
Hefei 230026
China