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\(q\)-extensions for the Apostol-Genocchi polynomials. (English) Zbl 1189.11016

Summary: In this paper, we define the Apostol-Genocchi polynomials and \(q\)-Apostol-Genocchi polynomials. We give the generating function and some basic properties of \(q\)-Apostol-Genocchi polynomials. Several interesting relationships are also obtained.

MSC:

11B83 Special sequences and polynomials
11M35 Hurwitz and Lerch zeta functions
11S40 Zeta functions and \(L\)-functions
33E20 Other functions defined by series and integrals
05A30 \(q\)-calculus and related topics
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