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Barnes' First Lemma and its Finite Analogue

Published online by Cambridge University Press:  20 November 2018

Anna Helversen-Pasotto  and
Patrick Solé
Anna Helversen-Pasotto
Affiliation:
U.N.S.A. Faculté des Sciences Département de Mathématiques CNRS-URA 168 Parc Valrose B.R 71 06108 NICE-CEDEX 2 France
Patrick Solé
Affiliation:
CNRS-URA 1376 Laboratoire 1.3.S, Bâtiment 4 250 rue Albert Einstein Sophia-Antipolis 06560 Valbonne France
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Abstract

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We give a parallel proof of Barnes' first lemma and of its finite analogue. In both cases we use the Mellin transform. In the classical case, the proof avoids the residue theorem. In the finite case the Gamma function is replaced by the Gaussian sum function and the beta function by the Jacobi sum function.

Keywords

33A1511L0520C99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 3 , 01 September 1993 , pp. 273 - 282
Copyright
Copyright © Canadian Mathematical Society 1993

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