Browse > Article
http://dx.doi.org/10.4134/CKMS.2013.28.3.457

ANALYTIC CONTINUATION OF WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS  

Araci, Serkan (Department of Mathematics Faculty of Arts and Science University of Gaziantep)
Acikgoz, Mehmet (Department of Mathematics Faculty of Arts and Science University of Gaziantep)
Gursul, Aynur (Department of Mathematics Faculty of Arts and Science University of Gaziantep)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.3, 2013 , pp. 457-462 More about this Journal
Abstract
In the present paper, we analyse analytic continuation of weighted $q$-Genocchi numbers and polynomials. A novel formula for weighted $q$-Genocchi-zeta function $\tilde{\zeta}_{G,q}(s{\mid}{\alpha})$ in terms of nested series of $\tilde{\zeta}_{G,q}(n{\mid}{\alpha})$ is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted $q$-Genocchi polynomials.
Keywords
Genocchi numbers and polynomials; q-Genocchi numbers and polynomials; weighted q-Genocchi numbers and polynomials; weighted q-Genocchi-zeta function;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 S. Araci, M. Acikgoz, and J. J. Seo, A study on the weighted q-Genocchi numbers and polynomials with their interpolation function, Honam Math. J. 34 (2012), no. 1, 11-18.   과학기술학회마을   DOI   ScienceOn
2 S. Araci, D. Erdal, and J. J. Seo, A study on the fermionic p-adic q-integral represen-tation on $\mathbb{Z}_p$ associated with weighted q-Bernstein and q-Genocchi polynomials, Abstr. Appl. Anal. 2011 (2011), Article ID 649248, 10 pages.
3 T. Kim, On explicit formulas of p-adic q-L-functions, Kyushu J. Math. 43 (1994), no. 1, 73-86.
4 T. Kim, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory 76 (1999), no. 2, 320-329.   DOI   ScienceOn
5 T. Kim, Power series and asymptotic series associated with the q-analog of the two-variable p-adic L-function, Russ. J. Math. Phys. 12 (2005), no. 2, 186-196.
6 T. Kim, On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl. 326 (2007), no. 2, 1458-1465.   DOI   ScienceOn
7 T. Kim, On the analogs of Euler numbers and polynomials associated with p-adic q-integral on $\mathbb{Z}_p$ at q =-1, J. Math. Anal. Appl. 331 (2007), no. 2, 779-792.   DOI   ScienceOn
8 T. Kim, Analytic continuation of q-Euler numbers and polynomials, Appl. Math. Lett. 21 (2008), no. 12, 1320-1323.   DOI   ScienceOn
9 T. Kim, On p-adic interpolating function for q-Euler numbers and its derivatives, J. Math. Anal. Appl. 339 (2008), no. 1, 598-608.   DOI   ScienceOn
10 T. Kim, C. S. Ryoo, L. C. Jang, and S. H. Rim, Exploring the q-Riemann zeta function and q-Bernoulli polynomials, Discrete Dyn. Nat. Soc. 2005 (2005), no. 2, 171-181.   DOI   ScienceOn