[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5831/HMJ.2010.32.4.563

CALCULATING ZEROS OF THE TWISTED (h, q)-EXTENSION OF GENOCCHI POLYNOMIALS

Ryoo, C.S. (Department of Mathematics, Hannam University)
Kim, T. (Division of General Education-Mathematics, Kwangwoon University)

Publication Information

Honam Mathematical Journal / v.32, no.4, 2010 , pp. 563-579 More about this Journal

Abstract

In this paper we introduce the new analogs of Genocchi numbers and polynomials. Finally, we investigate the zeros of the twisted (h,q)-extension of Genocchi polynomials ${G_{n,q,w}^{(h)}}$ (x).

Keywords

Genocchi numbers and polynomials; (h,q)-Genocchi numbers and polynomials; twisted (h,q)-extension of Genocchi numbers and polynomials; real and complex zeros;

Citations & Related Records

Reference

1	Kim, T., Jang, L.C., Pak, H-K.(2001). A note on q-Euler and Genocchi numbers, Proc. Japan Acad., v.77 A, pp. 139-141.
2	Kim, T., Ryoo, C.S., Jang, L.C., Rim, S.H.(2005). Exploring the q-Riemann Zeta function and q-Bernoulli polynomials , Discrete Dynamics in Nature and Society, v.2005(2), pp.171-181. DOI ScienceOn
3	Ryoo, C.S.(2009). A numerical computation on the structure of the roots of (h,q)-extension of Genocchi polynomials, Mathematical and Computer Modelling, v.49, pp. 463-474 DOI ScienceOn
4	Ryoo, C.S.(2008). Calculating zeros of the twisted Genocchi poly-nomiais, Advan. Stud. Contemp. Math., v.17(2). pp. 147-159.
5	Ryoo, C.S., Kim, T.(2009). Calculating zeros of the twisted q-Genocchi polynomials, Proceedings of the Jangjeon Mathematical Society, v.12(3), pp. 343-353.
6	Ryoo, C.S., Kim, T., Jang, L.C.(2007). Some relationships between the analogs of Euler numbers and polynomials, Journal of Inequalities and Applications, v.2007, Article ID 86052, 22 pages. DOI ScienceOn
7	Ryoo,C.S., Song, H., Agarwal, R.P. (2004). On the roots of the q-analogue of Euler-Barnes' polynomials, Advan. Stud. Contemp. Math., v.9, pp. 153-163.
8	Ryoo.C.S., Kim, T., Agarwal, R.P. (2005). The structure of the zeros of the generalized Bernoulli polynomials, Neural Parallel Sci. Comput., v.13, pp. 371-379.
9	Cenkci, M., Can, M., Kurt, V.(2004). q-adic interpolation functions and kummer type congruence for q-twisted and q-generalized twisted Euler numbers, Advan. Stud. Contemp. Math., v. 9, pp. 203-216.
10	Kreweras, G. (1997). An Additive Generation for the Genocchi Numbers and Two of its Enumerative Meanings, Bull. Inst. Combin. Appl., v.20, pp. 99-103.
11	Kim, T.(2002). q-Volkenborn integration, Russ. J. Math. Phys., v. 9, pp. 288-299.
12	Kim, T.(2007). On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl., v.326, pp. 1458-1465. DOI ScienceOn