DOI QR코드

DOI QR Code

SYMMETRY PROPERTIES FOR A UNIFIED CLASS OF POLYNOMIALS ATTACHED TO χ

  • Gaboury, S. (Department of Mathematics and Computer Science, University of Quebec at Chicoutimi) ;
  • Tremblay, R. (Department of Mathematics and Computer Science, University of Quebec at Chicoutimi) ;
  • Fugere, J. (Department of Mathematics and Computer Science, Royal Military College)
  • Received : 2012.01.24
  • Accepted : 2012.09.05
  • Published : 2013.01.30

Abstract

In this paper, we obtain some generalized symmetry identities involving a unified class of polynomials related to the generalized Bernoulli, Euler and Genocchi polynomials of higher-order attached to a Dirichlet character. In particular, we prove a relation between a generalized X version of the power sum polynomials and this unified class of polynomials.

Keywords

References

  1. A. Bayad, T. Kim, J. Choi, Y.H. Kim, and B. Lee, On the symmetry properties of the generalized higher order Euler polynomials, J. Appl. Math. & Informatics 29 (2011), 511-516.
  2. T. Kim, Symmetry p-adic invariant integral on ${\mathbb{Z}}_p$ for Bernoulli and Euler polynomials, Journal of Difference Equations and Applications 14 (12) (2008), 1267-1277. https://doi.org/10.1080/10236190801943220
  3. T. Kim, Symmetry properties of the generalized higher order Euler polynomials, Proc. Jangjeon Math. Soc. 13 (2010), 13-16.
  4. T. Kim and Y.-H. Kim, On the symmetric properties for the generalized twisted Bernoulli polynomials, Journal of Inequalities and Applications, Article ID 164743 (2009), 8 pages.
  5. T. Kim, B. Lee, and Y.-H. Kim, On the symmetric properties of the multivariate p-adic invariant integral on Zp associated with the twisted generalized Euler polynomials of higher order, Journal of Inequalities and Applications Article ID 826548 (2010), 8 pages.
  6. Y.H. Kim and K.-W. Hwang, A symmetry of power sum and twisted bernoulli polynomials, Adv. Stud. Contemp. Math. 18 (2009), 127-133.
  7. V. Kurt, A further symmetric relation on the analogue of the Apostol-Bernoulli and the analogue of the Apostol-Genocchi polynomials, Appl. Math. Sciences 3, 56 (2009), 2357-2364.
  8. H. Liu and W. Wang, Some identies on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums, Discrete Math. 309 (2009), 3346-3363. https://doi.org/10.1016/j.disc.2008.09.048
  9. Q.-M. Luo, Apostol-Euler polynomials of higher order and gaussian hypergeometric functions, Taiwanese J. Math. 10 (4) (2006), 917-925. https://doi.org/10.11650/twjm/1500403883
  10. Q.-M. Luo and H.M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math.Anal.Appl. 308 (1) (2005), 290-302. https://doi.org/10.1016/j.jmaa.2005.01.020
  11. Q.M. Luo and H.M. Srivastava, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. 51 (2006), 631-642. https://doi.org/10.1016/j.camwa.2005.04.018
  12. M. Ali Ozarslan, Unified Apostol-Bernoulli, Euler and Genocchi polynomials, Compu.Math.Appl. article in press (2012).
  13. H. Ozden, Unification of generating function of the Bernoulli, Euler and Genocchi numbers and polynomials, AIP Conference Proceedings 1281 (2010), 1125-1128.
  14. H. Ozden, Generating functions of the unified representation of the Bernoulli, Euler and Genocchi polynomials of higher order, AIP Conference Proceedings 1389 (2011), 349-352.
  15. H. Ozden, Y. Simsek, and H.M. Srivastava, A unified presentation of the generating function of the generalized Bernoulli, Euler and Genocchi polynomials, Comput. Math. Appl., 60 (2010), 2779-2787. https://doi.org/10.1016/j.camwa.2010.09.031
  16. C.S. Ryoo, T. Kim, J. Choi, and B. Lee, On the generalized q-Genocchi numbers and polynomials of higher order, Advances in Differences Equations, Article ID 424809 (2011), 8 pages.
  17. Y. Simsek, Complete sum of products of (h,q)-extension of Euler polynomials and numbers, Journal of Difference Equations and Applications 16 (11) (2010), 1331-1348. https://doi.org/10.1080/10236190902813967
  18. H.M. Srivastava and J. Choi, Series associated with zeta and related functions, Kluwer Academin Publishers, Dordrecht, Boston and London, 2001.
  19. L.C. Washington, Introduction to cyclotomic fields, Graduate Text in Mathematics, Springer-Verlag, New York, 83 (1982).
  20. Z. Zhang and H. Yang, Several identities for the generalized Apostol-Bernoulli polynomials, Comput. Math. Appl. 56 (2008), 2993-2999. https://doi.org/10.1016/j.camwa.2008.07.038