A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials

Computers and Mathematics with Applications

Volumn 60, Issue 10, 2010, Pages 2779-2787

  Ozden, Hacer ^a   Simsek, Yilmaz ^b   Srivastava, H M ^c  

^a ULUDAG UNIVERSITY   (Turkey)

^b AKDENIZ UNIVERSITY   (Turkey)

^c UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Bernoulli numbers and Bernoulli polynomials; Dirichlet character; Euler numbers and Euler polynomials; Genocchi numbers and Genocchi polynomials; HurwitzLerch zeta function; Lerch zeta function; LipschitzLerch zeta function; Mellin transformation; Polylogarithm function; Recurrence relations; Riemann and Hurwitz (or generalized) zeta functions

Indexed keywords

BERNOULLI POLYNOMIALS; DIRICHLET CHARACTERS; EULER NUMBERS; GENOCCHI NUMBERS AND GENOCCHI POLYNOMIALS; HURWITZ-LERCH ZETA FUNCTION; LERCH ZETA FUNCTION; MELLIN TRANSFORMATION; POLYLOGARITHM FUNCTIONS; RECURRENCE RELATIONS; ZETA FUNCTION;

FUNCTION EVALUATION; FUNCTIONS; POLYNOMIALS;

NUMBER THEORY;

EID: 78049294653     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.09.031     Document Type: Article

References (30)

1. J. Choi, P.J. Anderson, and H.M. Srivastava Carlitz's q-Bernoulli and q-Euler polynomials and a class of q-Hurwitz zeta functions Appl. Math. Comput. 215 2009 1185 1208
2. Q.-M. Luo, and H.M. Srivastava Some generalizations of the ApostolBernoulli and ApostolEuler polynomials J. Math. Anal. Appl. 308 2005 290 302
3. Y. Simsek, and H.M. Srivastava A family of p-adic twisted interpolation functions associated with the modified Bernoulli numbers Appl. Math. Comput. 216 2010 2976 2987
4. H.M. Srivastava Some formulas for the Bernoulli and Euler polynomials at rational arguments Math. Proc. Cambridge Philos. Soc. 129 2000 77 84
5. H.M. Srivastava, M. Garg, and S. Choudhary A new generalization of the Bernoulli and related polynomials Russian J. Math. Phys. 17 2010 251 261
6. H.M. Srivastava, and. Pintr Remarks on some relationships between the Bernoulli and Euler polynomials Appl. Math. Lett. 17 2004 375 380
7. B.K. Karande, and N.K. Thakare On the unification of Bernoulli and Euler polynomials Indian J. Pure Appl. Math. 6 1975 98 107
8. I.N. Cangul, H. Ozden, and Y. Simsek Generating functions of the (h, q) extension of twisted Euler polynomials and numbers Acta Math. Hungar. 120 2008 281 299
9. H. Ozden, Unification of generating function of the Bernoulli, Euler and Genocchi numbers and polynomials, in: Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, Amer. Inst. Phys. Conf. Proc. (2010) (in press).
10. H. Ozden, and Y. Simsek A new extension of q-Euler numbers and polynomials related to their interpolation functions Appl. Math. Lett. 21 2008 934 939
11. Y.-H. Kim, W. Kim, and L.-C. Jang On the q-extension of Apostol-Euler numbers and polynomials Abstr. Appl. Anal. 2008 2008 1 10 Article ID 296159
12. Q.-M. Luo q-Extensions for the ApostolGenocchi polynomials Gen. Math. 17 2009 113 125
13. Y. Simsek q-Analogue of the twisted L-series and q-twisted Euler numbers J. Number Theory 110 2005 267 278
14. Y. Simsek Theorems on twisted L-functions and twisted Bernoulli numbers Adv. Stud. Contemp. Math. 11 2005 205 218
15. Y. Simsek Twisted (h, q) -Bernoulli numbers and polynomials related to twisted (h, q) -zeta function and L-function J. Math. Anal. Appl. 324 2006 790 804
16. T.M. Apostol On the Lerch zeta function Pacific J. Math. 1 1951 161 167
17. T. Kim, S.-H. Rim, Y. Simsek, and D. Kim On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions J. Korean Math. Soc. 45 2008 435 453
18. Y. Simsek Twisted p-adic (h, q) -L-functions Comput. Math. Appl. 59 2010 2097 2110
19. H.M. Srivastava, and J. Choi Series Associated with the Zeta and Related Functions 2001 Kluwer Academic Publishers Dordrecht, Boston, London
20. E.T. Whittaker, and G.N. Watson A Course of Modern Analysis: An Introduction to the General Theory Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions fourth ed. 1962 Cambridge University Press Cambridge, London, New York
21. L. Carlitz Some generalized multiplication formulae for the Bernoulli polynomials and related functions Monatsh. Math. 66 1962 1 8
22. H.M. Srivastava, T. Kim, and Y. Simsek q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series Russian J. Math. Phys. 12 2005 241 268
23. A.A. Aygunes, Y. Simsek, Remarks on interpolation function of higher order (h, q) -Bernoulli numbers, in: Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (2009), Amer. Inst. Phys. Conf. Proc., vol. 1168, 2009, pp. 6164.
24. M. Garg, K. Jain, and H.M. Srivastava Some relationships between the generalized ApostolBernoulli polynomials and HurwitzLerch Zeta functions Integral Transforms Spec. Funct. 17 2006 803 815
25. S.-D. Lin, H.M. Srivastava, and P.-Y. Wang Some expansion formulas for a class of generalized HurwitzLerch Zeta functions Integral Transforms Spec. Funct. 17 2006 817 822
26. J. Choi, D.S. Jang, and H.M. Srivastava A generalization of the HurwitzLerch Zeta function Integral Transforms Spec. Funct. 19 2008 65 79
27. D. Rducanu, and H.M. Srivastava A new class of analytic functions defined by means of a convolution operator involving the HurwitzLerch Zeta function Integral Transforms Spec. Funct. 18 2007 933 943
28. P.L. Gupta, R.C. Gupta, S.-H. Ong, and H.M. Srivastava A class of HurwitzLerch Zeta distributions and their applications in reliability Appl. Math. Comput. 196 2008 521 531
29. J. Choi, P.J. Anderson, and H.M. Srivastava Some q-extensions of the ApostolBernoulli and the ApostolEuler polynomials of order n, and the multiple Hurwitz zeta function Appl. Math. Comput. 199 2008 723 737
30. J. Choi, and H.M. Srivastava Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals Math. Nachr. 282 2009 1709 1723