A NOTE ON GENOCCHI-ZETA FUNCTIONS

• Journal title : Honam Mathematical Journal
• Volume 31, Issue 3,  2009, pp.399-405
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2009.31.3.399
Title & Authors
A NOTE ON GENOCCHI-ZETA FUNCTIONS
Park, Kyoung-Ho;

Abstract
In this paper, we study the Genoochi-zeta functions which are entire functions in whole complex s-plane these zeta functions have the values of the Genocchi numbers and the Genoochi polynomials at negative integers respectively. That is ${\zeta}_G(1-k) Keywords Genocchi numbers;Genocchi polynomials;Genocchi-Zeta function; Language English Cited by References 1. H. M. Srivastava, T. Kim and Y. Simsek, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series, Russ. J. Math. Phys. 12 (2005), no. 2, 241-268. 2. H. Ozden, Y. Simsek, I. N. Cangul and S.-H. Rim, A note on p-adic q-Euler measure, Adv. Stud. Contemp. Math. 14 (2007), 233-239. 3. K. Shiratani, S. Yamamoto, On a p-adic interpolating function for the Euler numbers and its derivatives, Mem. Fac. Sci. Kyushu Univ. Ser. A 39 (1985), 113-125. 4. L.-C. Jang, T. Kim, D-H. Lee, and AD-W. Park An application of polylogarithms in analogs of Genocchi numbers, NNTDM: Notes Number Theory and Discrete Math. 7 (2001), no. 3, 65-70. 5. L.-C. Jang and T. Kim, q-Genocchi Numbers and Polynomials Associated with. Fermionic p-Adic Invariant Integrals on Zp, Abstract and Applied Analysis, vol. 2008, Article ID 232187, 8 pages, 2008. doi:10.1155/2008/232187. 6. M. Cenkci, V.Kurt, p-udic interpolation function and Kummer type congruence for q-twisted Euler numbers, Adv. Stud. Contemp. Math. 9 (2004), 203-216. 7. M. Schork, Ward's "calculus of sequence", q-calculus and the limit q${\rightarrow}$-1, Adv. St ud. Contemp. Math. 13 (2006), 131-141. 8. M. Schork, Combinatorial aspects of normal ordering and its connection to q-calculus, Adv. Stud. Contemp. Math. 15 (2007), 49-57. 9. S.-H. Rim and T. Kim, A note on p-adic Euler measure on${\mathbb{Z}}_p$, Russ. J. Math. Phys. 13 (2006), no. 3, 358-361. 10. T. Kim, L.-C. Jang and H. K. Pak, A note on q-Euler and Genocchi numbers, Proc. Japan Acad. 77, Ser. A (2001), 139-141. 11. T. Kim, q-Volkenbom integration, Russ. J. Math. Phys. 9 (2002), no. 3, 288-299. 12. T. Kim, Non-Archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys. 10 (2003), no. 1, 91-98. 13. T. Kim, On Euler-Barnes multiple zeta functions, Russ. J. Math. Phys. 10 (2003), no. 3, 261-267. 14. T. Kim, Analytic continuation of multiple q-zeta functions and their values at negative integers, Russ. J. Math. Phys. 11 (2004), no. 1, 71-76. 15. T. Kim et al, Introduction to Non-Archimedian Analysis, Kyo Woo Sa (Korea), 2004. (http://www.kyowoo.co.kr). 16. T. Kim, A note on q-Volkenborn integration, Proc. Jangjeon Math. Soc. 8 (2005), 13-17. 17. T. Kim, Power series and asymptotic series associated with the q-analog of the two-variable p-adic L-function, Russ. J. Math. Phys. 12 (2005), no. 2, 186-196. 18. T. Kim, Multiple p-adic L-function, Russ. J. Math. Phys. 13 (2006), no. 2, 151-157. 19. T. Kim, q-generalized Euler numbers and polynomials, Russ. J. Math. Phys. 13 (2006). no. 3, 293-298. 20. T. Kim, Euler numbers and polynomials associated with zeta functions, Abstract and Applied Analysis, 2008 (2008), Article ID 581582, 11 pages. 21. T. Kim, The modified q-Euler numbers and polynomials, Adv. Stud. Contemp. Math. 16 (2008), 161-170. 22. T. Kim, A note on p-adic q-integml on${\mathbb{Z}}_p$Associated with q-Euler numbers, Adv. Stud. Contemp. Math. 15 (2007), 133-138. 23. T. Kim, J. Y. Choi and J. Y. Sug, Ext ended q-Euier numbers and polynomials associat ed with fermionic p-adic q-integral on${\mathbb{Z}}_p$, Russ. J . Math. Phys. 14 (2007), no. 2, 160-163. 24. T. Kim. On the analogs of Euler numbers and polynomials associated with p-adic q-integral on${\mathbb{Z}}_p\$ at q = -1, Journal of Mathematical Analysis and Applications. vol. 331 (2007), no. 2, 779-792.

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