Integral representations of q-analogues of the Hurwitz zeta function

Abstract

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this q-analogue. All the discussion developed here is entirely different from the previous work in [4]

14 pages

References in corpus (4)

• Multiple $q$-Zeta Values
• q-Multiple Zeta Functions and q-Multiple Polylogarithms
• q-Analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function
• Hierarchy of the Selberg zeta functions

Cited by in corpus (5)

• Infinite series involving hyperbolic functions
• Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and $q$-zeta functions
• Nonstandard Mathematics and New Zeta and L-Functions
• On q-analogues of quadratic Euler sums
• Identities for the q-harmonic numbers and q-binomial coefficients