ANALYTIC CONTINUATION OF WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS

Title & Authors
ANALYTIC CONTINUATION OF WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS
Araci, Serkan; Acikgoz, Mehmet; Gursul, Aynur;

Abstract
In the present paper, we analyse analytic continuation of weighted $\small{q}$-Genocchi numbers and polynomials. A novel formula for weighted $\small{q}$-Genocchi-zeta function $\small{\tilde{\zeta}_{G,q}(s{\mid}{\alpha})}$ in terms of nested series of $\small{\tilde{\zeta}_{G,q}(n{\mid}{\alpha})}$ is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted $\small{q}$-Genocchi polynomials.
Keywords
Genocchi numbers and polynomials;q-Genocchi numbers and polynomials;weighted q-Genocchi numbers and polynomials;weighted q-Genocchi-zeta function;
Language
English
Cited by
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Kyungpook mathematical journal, 2014. vol.54. 1, pp.131-141
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A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order, Kyungpook mathematical journal, 2014, 54, 1, 131
2.
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