Abstract
Integral representations of $q$-analogues of the Barnes multiple zeta functions are studied. The integral representation provides a meromorphic continuation of the $q$-analogue to the whole plane and describes its poles and special values at non-positive integers. Moreover, for any weight, employing the integral representation, we show that the $q$-analogue converges to the Barnes multiple zeta function when $q \uparrow 1$ for all complex numbers.
Information
Published: 1 January 2007
First available in Project Euclid: 27 January 2019
zbMATH: 1219.11138
MathSciNet: MR2405619
Digital Object Identifier: 10.2969/aspm/04910545
Subjects:
Primary:
11M41
Secondary:
11B68
Keywords:
$q$-analogue
,
Barnes' multiple Bernoulli polynomial
,
Barnes' multiple zeta function
,
classical limit
,
Contour integral
Rights: Copyright © 2007 Mathematical Society of Japan
