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http://dx.doi.org/10.4134/BKMS.2010.47.3.575

A NEW APPROACH TO q-GENOCCHI NUMBERS AND POLYNOMIALS  

Kurt, Veli (Department of Mathematics Akdeniz University)
Cenkci, Mehmet (Department of Mathematics Akdeniz University)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.3, 2010 , pp. 575-583 More about this Journal
Abstract
In this paper, new q-analogs of Genocchi numbers and polynomials are defined. Some important arithmetic and combinatoric relations are given, in particular, connections with q-Bernoulli numbers and polynomials are obtained.
Keywords
q-exponential functions; q-Genocchi numbers and polynomials; q-Bernoulli numbers and polynomials;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 5
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1 T. Kim, A note on p-adic q-integral on $Z_p$ associated with q-Euler numbers, Adv. Stud. Contemp. Math. (Kyungshang) 15 (2007), no. 2, 133-137.
2 T. Kim, q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys. 14 (2007), no. 1, 15-27.   DOI
3 T. Kim, L.-C. Jang, and H.-K. Pak, A note on q-Euler and Genocchi numbers, Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 8, 139-141.   DOI
4 T. Kim, M.-S. Kim, L.C. Jang, and S.-H. Rim, New q-Euler numbers and polynomials associated with p-adic q-integrals, Adv. Stud. Contemp. Math. (Kyungshang) 15 (2007), no. 2, 243-252.
5 T. H. Koornwinder, Special functions and q-commuting variables, Special functions, qseries and related topics (Toronto, ON, 1995), 131-166, Fields Inst. Commun., 14, Amer. Math. Soc., Providence, RI, 1997.
6 B. A. Kupershmidt, Reflection symmetries of q-Bernoulli polynomials, J. Nonlinear Math. Phys. 12 (2005), suppl. 1, 412-422.   DOI
7 Y. Simsek, I. N. Cangul, V. Kurt, and D. Kim, q-Genocchi numbers and polynomials associated with q-Genocchi-type l-functions, Adv. Difference Equ. 2008 (2008), Art. ID 815750, 12 pp. doi:10.11555.2008/85750.
8 A. De Sole and V. Kac, On integral representations of q-gamma and q-beta functions, arXiv:math QA/0302032.
9 H. M. Srivastava and A. Pinter, Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett. 17 (2004), no. 4, 375-380.   DOI   ScienceOn
10 L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987-1000.   DOI
11 T. Kim, A note on the q-Genocchi numbers and polynomials, J. Inequal. Appl. 2007 (2007), Art. ID 71452, 8 pp. doi:10.1155/2007/71452.
12 T. Kim, On the multiple q-Genocchi and Euler numbers, Russ. J. Math. Phys. 15 (2008), no. 4, 481-486.   DOI
13 T. Kim, Note on q-Genocchi numbers and polynomials, Adv. Stud. Contemp. Math. (Kyungshang) 17 (2008), no. 1, 9-15.
14 A. S. Hegazi and M. Mansour, A note on q-Bernoulli numbers and polynomials, J. Nonlinear Math. Phys. 13 (2006), no. 1, 9-18.   DOI
15 M. Cenkci, M. Can, and V. Kurt, q-extensions of Genocchi numbers, J. Korean Math. Soc. 43 (2006), no. 1, 183-198.   DOI   ScienceOn
16 G. Gasper, Lecture notes for an introductory minicourse on q-series, arXiv.math.CA/9509223.
17 G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
18 L. C. Jang and T. Kim, q-Genocchi numbers and polynomials associated with fermionic p-adic invariant integrals on Zp, Abstr. Appl. Anal. 2008 (2008), Art. ID 232187, 8 pp. doi:10.1155/2008/232187.
19 L. C. Jang, T. Kim, D. H. Lee, and D. W. Park, An application of polylogarithms in the analogue of Genocchi numbers, NNTDM 7 (2000), 66-70.
20 V. Kac and P. Cheung, Quantum Calculus, Springer Verlag, New York, 2002.
21 T. Kim, q-generalized Euler numbers and polynomials, Russ. J. Math. Phys. 13 (2006), no. 3, 293-298.   DOI
22 T. Kim, On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl. 326 (2007), no. 2, 1458-1465.   DOI   ScienceOn