A family of multiple integrals analytically solvable
type: Item
instance of: scholarly article
title: A family of multiple integrals analytically solvable
zbMATH Open document ID: 0937.33002
DOI: 10.1016/S0893-9659(98)00136-0
published in: Applied Mathematics Letters
publication date: 2000-06-13T00:00:00Z
review text: Starting from the integral definition of the beta function \(\beta(a,b)\), and performing the analytic continuation in \(a,b\) from the region \(\operatorname {Re} a>-1\), \(\operatorname {Re}b<1\), where the ordinary expression for the integral converges, to the rest of the complex plane, for the two variables \(a\), \(b\), and by further extending the method to multiple integrals of this sort, the author is able to device a procedure that allows him to obtain, in quite an ingenious way, a number of new series and integrals which appear in quantum field theory and statistical physics. The method is somehow reminiscent of the zeta function regularization procedure, but the particular way chosen by the author to perform the analytic continuations actually adds new insights to this field.
reviewed by: Emilio Elizalde
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 32A70
zbMATH DE Number: 1370085
zbMATH Keywords: multiple integral
zbMATH Keywords: beta function
zbMATH Keywords: analytic continuation
author: José L. López
MaRDI profile type: Publication
cites work: Ten Physical Applications of Spectral Zeta Functions
cites work: The stress tensor conformal anomaly and analytic regularizations
cites work: Quantum field theory.
cites work: Q3661894
cites work: Q3744481
full work available at URL: s0893-9659(98)00136-0
OpenAlex ID: W1977978551
description: scientific article; zbMATH DE number 1370085