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http://dx.doi.org/10.5666/KMJ.2015.55.1.29

Functional Equations associated with Generalized Bernoulli Numbers and Polynomials  

Ryoo, Cheon Seoung (Department of Mathematics, Hannam University)
Dolgy, Dmitry Victorovich (Hanrimwon, Kwangwoon University, Korea School of Natural Sciences, Far Eeastern Federal University)
Kwon, Hyuck In (Department of Mathematics, Kwangwoon University)
Jang, Yu Seon (Department of Applied Mathematics, Kangnam University)
Publication Information
Kyungpook Mathematical Journal / v.55, no.1, 2015 , pp. 29-39 More about this Journal
Abstract
In this paper, we investigate the functional equations of the multiple Dirichlet and Hurwitz L-functions associated with Bernoulli numbers and polynomials attached to Dirichlet character.
Keywords
Euler zeta function; Dirichlet L-series; Hurwitz L-function; Generalized Bernoulli numbers and polynomials attached to ${\chi}$;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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1 L. V. Ahlfors, Complex Analysis, 3rd Edition, McGraw-Hill, 1979.
2 A. Bayad, Modular properties of elliptic Bernoulli and Euler functions, Adv. Stud. Contemp. Math., 20(3)(2010), 389-401.
3 A. Bayad and T. Kim, Identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials, Adv. Stud. Contemp. Math., 20(2)(2010), 247-253.
4 J. Choi, D. S. Kim, T. Kim, and Y. H. Kim, Some arithmetic identities on Bernoulli and Euler numbers arising from the p-adic integrals on ${\mathbb{Z}}_p$, Adv. Stud. Contemp. Math., 22(2)(2012), 239-247.
5 R. J. Dwilewicz and J. Minac, Values of the Riemann zeta function at integers, Materials Matematics 2009, no. 6, 1-26.
6 K. W. Hwang, D. V. Dolgy, D. S. Kim, T. Kim, and S. H. Lee, Some theorems on Bernoulli and Euler numbers, Ars Combin., 109(2013), 285-297.
7 L. C. Jang and H. K. Pak, Non-Archimedean integration associated with q-Bernoulli numbers, Proc. Jangjeon math. Soc., 5(2)(2002), 125-129.
8 D. Kang, J. Jeong, S. J. Lee, and S. H. Rim, A note on the Bernoulli polynomials arising from a non-linear differential equation, Proc. Jangjeon math. Soc., 16(1)(2013), 37-43.
9 T. Kim, J. Choi and Y. H. Kim, A note on the values of Euler zeta functions at positive integers, Adv. Stud. Contemp. Math., 22(1)(2012), 27-34.
10 T. Kim, D. S. Kim, A. Bayad, and S. H. Rim, Identities on the Bernoulli and the Euler numbers and polynomials, Ars Combin., 107(2012), 455-463.
11 G. Kim, B. Kim and J. Choi, The DC algorithm for computing sums of powers of consecutive integers and Bernoulli numbers, Adv. Stud. Contemp. Math., 17(2)(2008), 137-145.
12 A. Kudo, A congruence of generalized Bernoulli number for the character of the first kind, Adv. Stud. Contemp. Math., 2(2000), 1-8.
13 B. Kurt, Some identities on the second kind Bernoulli polynomials of order ${\alpha}$ and second kind Euler polynomials of order ${\alpha}$ with the parameters a; b; c, Proc. Jangjeon Math. Soc., 16(2)(2013), 245-249.
14 Q. M. Luo, Some recursion formulae and relations for Bernoulli numbers and Euler numbers of higher order, Adv. Stud. Contemp. Math., 10(1)(2005), 63-70.
15 Q. M. Luo and F. Qi, Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials, Adv. Stud. Contemp. Math., 7(1)(2003), 11-18.
16 H. Ozden, I. N. Cangul and Y. Simsek, Remarks on q-Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp. Math., 18(1)(2009), 41-48.
17 J. W. Park, S. H. Rim, J. Seo, and J. Kwon, A note on the modified q-Bernoulli polynomials, Proc. Jangjeon math. Soc., 16(4)(2013), 451-456.
18 Y. Simsek, Theorems on twisted L-function and twisted Bernoulli numbers, Adv. Stud. Contemp. Math., 11(2)(2005), 205-218.
19 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(2)(2005), 241-268.
20 L. C.Washington, Introduction to cyclotomic fields, Springer-Verlag, New York, 1997.
21 Z. Zhang and H. Yang, Some closed formulas for generalized Bernoulli-Euler numbersand polynomials, Proc. Jangjeon Math. Soc., 11(2)(2008), 191-198.