[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2013.26.1.231

CERTAIN RESULTS ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS

Seo, Jong Jin (Department of Applied Mathematics Pukyong National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.26, no.1, 2013 , pp. 231-242 More about this Journal

Abstract

In this work, we deal with $q$ -Genocchi numbers and polynomials. We derive not only new but also interesting properties of the $q$ -Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the $q$ -Genocchi polynomials and derive distribution formula for the $q$ -Genocchi polynomials. In the final part, we introduce a definition of $q$ -Zeta-type function which is interpolation function of the $q$ -Genocchi polynomials at negative integers which we express in the present paper.

Keywords

Genocchi numbers and polynomials; q-Genocchi numbers and polynomials with weight 0; p-adic q-integral on ${\mathbb{Z}}_p$ ;

Citations & Related Records

Reference

1	S. Araci, D. Erdal, and J. J. Seo, A study on the fermionic p-adic q-integral representation on $\mathbb{Z}_p$ associated with weighted q-Bernstein and q-Genocchi polynomials, Abstract and Applied Analysis, 2011 (2011), Article ID 649248, 10 pages.
2	S. Araci, J. J. Seo, and D. Erdal, New Construction weighted (h,q)-Genocchi numbers and polynomials related to Zeta type function, Discrete Dynamics in Nature and Society, 2011 (2011), Article ID 487490, 7 pages.
3	S. Araci, M. Acikgoz, and Feng Qi, On the q-Genocchi numbers and polynomials with weight zero and their applications, Available at http://arxiv.org/abs/1202.2643
4	S. Araci, Novel Identities for q-Genocchi Numbers and Polynomials, Journal of Function Spaces and Applications 2012 (2012), Article ID 214961, 13 pages.
5	S. Araci, M. Acikgoz and J. J. Seo, Explicit formulas involving q-Euler numbers and polynomials, Abstract and Applied Analysis 2012 (2012), Article ID 298531, 11 pages (Article in press).
6	Y. He and C. Wang, Some Formulae of Products of the Apostol-Bernoulli and Apostol-Euler Polynomials, Discrete Dynamics in Nature and Society 2012 (2012), Article ID 927953, 11 pages.
7	T. Kim, Euler numbers and polynomials associated with Euler Zeta functions, Abstract and Applied Analysis 2008 (2008), Article ID 581582, 11 pages.
8	T. Kim and S.-H. Lee, Some Properties on the q-Euler Numbers and Polynomials, Abstract and Applied Analysis 2012 (2012), Article ID 284826, 9 pages, 2012.
9	D. Kim, T. Kim, S. -H. Lee, D. V. Dolgy, S.-H. Rim, Some new identities on the Bernoulli numbers and polynomials, Discrete Dynamics in Nature and Society 2011 (2011), Article ID 856132, 11 pages.
10	T. Kim, J. Choi, and Y. H. Kim, Some identities on the q-Bernoulli numbers and polynomials with weight 0; Abstract And Applied Analysis 2011 (2011), Article ID 361484, 8 pages.
11	T. Kim, On a q-analogue of the p-adic log gamma functions related integrals, J. Number Theory 76 (1999) no. 2, 320-329. DOI ScienceOn
12	T. Kim, and J. Choi, On the q-Euler numbers and polynomials with weight 0, Abstract and Applied Analysis 2012 (2012), Article ID 795304, 7 pages..
13	T. Kim, On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl. 326 (2007), 1458-1465. DOI ScienceOn
14	T. Kim, On the multiple q-Genocchi and Euler numbers, Russian J. Math. Phys. 15 (2008), no. 4, 481-486. DOI ScienceOn
15	T. Kim, On the weighted q-Bernoulli numbers and polynomials, Advanced Studies in Contemporary Mathematics 21 (2011), no. 2, 207-215.
16	T. Kim, q-Volkenborn integration, Russ. J. Math. phys. 9 (2002), 288-299.
17	T. Kim, q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys. 14 (2007), no. 1, 15-27. DOI
18	T. Kim, New approach to q-Euler polynomials of higher order, Russ. J. Math. Phys. 17 (2010), no. 2, 218-225. DOI ScienceOn
19	T. Kim, Some identities on the q-Euler polynomials of higher order and q- Stirling numbers by the fermionic p-adic integral on $\mathbb{Z}_p$ , Russ. J. Math. Phys. 16 (2009), no. 4, 484-491. DOI ScienceOn
20	D. Kim, T. Kim, J. Choi, and Y. H. Kim, Identities involving q-Bernoulli and q- Euler numbers, Abstract and Applied Analysis 2012 (2012), Article ID 674210, 10 pages.
21	C. S. Ryoo, A note on the weighted q-Euler numbers and polynomials, Advan. Stud. Contemp. Math. 21 (2011), 47-54.
22	I. N. Cangul, V. Kurt, H. Ozden, and Y. Simsek, On the higher-order w-q-genocchi numbers, Advanced Studies in Contemporary Mathematics 19 (2009), no. 1, 39-57.
23	M. Acikgoz, S. Araci and I. N. Cangul, A note on the modified q-Bernstein polynomials for functions of several variables and their reflections on q-Volkenborn integration, Applied Mathematics and Computation 218 (2011), no. 3, 707-712.