On the modified q-Genocchi numbers and polynomials and their applications

Abstract

The main objective of this paper is to introduce the modified q-Genocchi polynomials and to define their generating function. In the paper, we show new relations, which are explicit formula, derivative formula, multiplication formula, and some others, for mentioned q-Genocchi polynomials. By applying Mellin transformation to the generating function of the modified q-Genocchi polynomials, we define q-Genocchi zeta-type functions which are interpolated by the modified q-Genocchi polynomials at negative integers.

10 pages; submitted

References in corpus (5)

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• Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind
• Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
• Generating functions for q-Bernstein, q-Meyer-Konig-Zeller and q-Beta basis
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