Abstract
Recently, many mathematicians have studied various kinds of the -analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009.", Kim defined new generating functions of -Genocchi, -Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type -zeta function. This function interpolates -Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.
Highlights
Let p be a fixed odd prime number
When one talks of q-extension, q is variously considered as an indeterminate, a complex q ∈ C or a p-adic number q ∈ Cp
If q ∈ Cp, we assume that |q − 1|p < 1
Summary
Many mathematicians have studied various kinds of the q-analogue of Genocchi numbers and polynomials. In the work New approach to q-Euler, Genocchi numbers and their interpolation functions, “Advanced Studies in Contemporary Mathematics, vol 18, no. 105– 112, 2009.”, Kim defined new generating functions of q-Genocchi, q-Euler polynomials, and their interpolation functions. We give another definition of the multiple Hurwitz type qzeta function. This function interpolates q-Genocchi polynomials at negative integers. We give some identities related to these polynomials
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