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

Luo, Qiu-Ming

Gen. Math. 17, No. 2, 113-125 (2009).

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

Keywords:

\(q\)-Genocchi polynomials; \(q\)-Apostol-Genocchi polynomials; \(q\)-Hurwitz-Lerch zeta function; \(q\)-Goyal-Laddha-Hurwitz-Lerch zeta function