On q-analogs of zeta functions associated with a pair of q-analogs of Bernoulli numbers and polynomials

Abstract

In this paper, we use two different approaches to introduce q-analogs of Riemann’s zeta function and prove that their values at even integers are related to the q-Bernoulli and q-Euler’s numbers introduced by Ismail and Mansour [Analysis and Applications, 17(6) (2019), 853–895].

Mathematics Subject Classification (2020):

• 11B68
• 33E99

Key words:

• q-Bernoulli and Euler numbers
• q-zeta function
• contour integration
• Rayleigh functions