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Abstract and Applied Analysis
Volume 2013, Article ID 293532, 6 pages
http://dx.doi.org/10.1155/2013/293532
Research Article

Some Identities on the Generalized q-Bernoulli, q-Euler, and q-Genocchi Polynomials

1National Institute for Mathematical Sciences, Yuseong-daero 1689-gil, Yuseong-gu, Daejeon 305-811, Republic of Korea
2Department of Mathematics, Akdeniz University, 07058 Antalya, Turkey

Received 13 September 2013; Accepted 12 November 2013

Academic Editor: Junesang Choi

Copyright © 2013 Daeyeoul Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Choi, P. J. Anderson, and H. M. Srivastava, “Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function,” Applied Mathematics and Computation, vol. 199, no. 2, pp. 723–737, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  2. N. I. Mahmudov, “On a class of q-Bernoulli and q-Euler polynomials,” Advances in Difference Equations, vol. 2013, article 108, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  3. L. Carlitz, “q-Bernoulli numbers and polynomials,” Duke Mathematical Journal, vol. 15, pp. 987–1050, 1948. View at Google Scholar · View at MathSciNet
  4. L. Carlitz, “Expansions of q-Bernoulli numbers,” Duke Mathematical Journal, vol. 25, pp. 355–364, 1958. View at Google Scholar · View at MathSciNet
  5. M. Cenkci, M. Can, and V. Kurt, “q-extensions of Genocchi numbers,” Journal of the Korean Mathematical Society, vol. 43, no. 1, pp. 183–198, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. Cenkci, V. Kurt, S. H. Rim, and Y. Simsek, “On (i, q) Bernoulli and Euler numbers,” Applied Mathematics Letters, vol. 21, no. 7, pp. 706–711, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  7. G.-S. Cheon, “A note on the Bernoulli and Euler polynomials,” Applied Mathematics Letters, vol. 16, no. 3, pp. 365–368, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  8. T. Kim, “Some formulae for the q-Bernoulli and Euler polynomials of higher order,” Journal of Mathematical Analysis and Applications, vol. 273, no. 1, pp. 236–242, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. B. Kurt, “A further generalization of the Bernoulli polynomials and on the 2D-Bernoulli polynomials Bn,q(α),” Applied Mathematical Sciences, vol. 4, no. 47, pp. 2315–2322, 2010. View at Google Scholar · View at MathSciNet
  10. V. Kurt, “A new class of generalized q-Bernoulli and q-Euler polynomials,” in Proceedings of the International Western Balkans Conference of Mathematical Sciences, Elbasan, Albania, May 2013.
  11. Q.-M. Luo, “Some results for the q-Bernoulli and q-Euler polynomials,” Journal of Mathematical Analysis and Applications, vol. 363, no. 1, pp. 7–18, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Q.-M. Luo and H. M. Srivastava, “Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials,” Computers & Mathematics with Applications, vol. 51, no. 3-4, pp. 631–642, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  13. Q.-M. Luo and H. M. Srivastava, “q-extensions of some relationships between the Bernoulli and Euler polynomials,” Taiwanese Journal of Mathematics, vol. 15, no. 1, pp. 241–257, 2011. View at Google Scholar · View at MathSciNet
  14. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic, London, UK, 2001. View at MathSciNet
  15. H. M. Srivastava and A. Pintér, “Remarks on some relationships between the Bernoulli and Euler polynomials,” Applied Mathematics Letters, vol. 17, no. 4, pp. 375–380, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  16. P. Natalini and A. Bernardini, “A generalization of the Bernoulli polynomials,” Journal of Applied Mathematics, no. 3, pp. 155–163, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  17. R. Tremblay, S. Gaboury, and B.-J. Fugère, “A new class of generalized Apostol-Bernoulli polynomials and some analogues of the Srivastava-Pintér addition theorem,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1888–1893, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  18. R. Tremblay, S. Gaboury, and B. J. Fegure, “Some new classes of generalized Apostol Bernoulli and Apostol-Genocchi polynomials,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 182785, 14 pages, 2012. View at Publisher · View at Google Scholar
  19. S. Gaboury and B. Kurt, “Some relations involving Hermite-based Apostol-Genocchi polynomials,” Applied Mathematical Sciences, vol. 6, no. 81–84, pp. 4091–4102, 2012. View at Google Scholar · View at MathSciNet
  20. N. I. Mahmudov, “q-analogues of the Bernoulli and Genocchi polynomials and the Srivastava-Pintér addition theorems,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 169348, 8 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. N. I. Mahmudov and M. E. Keleshteri, “On a class of generalized q-Bernoulli and q-Euler polynomials,” Advances in Difference Equations, vol. 2013, article 115, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  22. S. Araci, J. J. Seo, and M. Acikgoz, “A new family of q-analogue of Genocchi polynomials of higher order,” Kyungpook Mathematical Journal. In press.
  23. B. A. Kupershmidt, “Reflection symmetries of q-Bernoulli polynomials,” Journal of Nonlinear Mathematical Physics, vol. 12, no. 1, pp. 412–422, 2005. View at Publisher · View at Google Scholar · View at MathSciNet