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On Barnes' Multiple Zeta and Gamma Functions

✍ Scribed by S.N.M. Ruijsenaars

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 215 KB
Volume: 156
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2000.1946

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✦ Synopsis

We show how various known results concerning the Barnes multiple zeta and gamma functions can be obtained as specializations of simple features shared by a quite extensive class of functions. The pertinent functions involve Laplace transforms, and their asymptotics is obtained by exploiting this. We also demonstrate how Barnes' multiple zeta and gamma functions fit into a recently developed theory of minimal solutions to first order analytic difference equations. Both of these new approaches to the Barnes functions give rise to novel integral representations. 2000 Academic Press Contents. 1. Introduction. 2. Generalized Barnes functions. 3. Barnes' multiple zeta and gamma functions. 4. The difference equation perspective. Appendix. A. First order difference equations.

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