Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 214961, 13 pages
http://dx.doi.org/10.1155/2012/214961
Research Article

Novel Identities for 𝑞 -Genocchi Numbers and Polynomials

Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaziantep, Turkey

Received 26 February 2012; Revised 25 April 2012; Accepted 9 May 2012

Academic Editor: Gestur Ólafsson

Copyright © 2012 Serkan Araci. 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. S. Araci, D. Erdal, and J.-J. Seo, “A study on the fermionic p-adic q-integral representation on Zp associated with weighted q-bernstein and q-genocchi polynomials,” Abstract and Applied Analysis, vol. 2011, Article ID 649248, 10 pages, 2011. View at Google Scholar
  2. S. Araci, J. J. Seo, and D. Erdal, “New construction weighted (h,q)-Genocchi numbers and polynomials related to zeta type functions,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 487490, 7 pages, 2011. View at Publisher · View at Google Scholar
  3. S. Araci, M. Acikgoz, and F. Qi, “On the q-Genocchi numbers and polynomials with weight zero and their applications,” Number Theory, http://arxiv.org/abs/1202.2643.
  4. T. Kim, B. Lee, S. H. Lee, and S.-H. Rim, “Identities for the Bernoulli and Euler numbers and polynomials,” Ars Combinatoria. In press.
  5. D. S. Kim, T. Kim, S.-H. Lee, D. V. Dolgy, and S.-H. Rim, “Some new identities on the Bernoulli and Euler numbers,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 856132, 11 pages, 2011. View at Publisher · View at Google Scholar
  6. T. Kim, J. Choi, and Y. H. Kim, “Some identities on the q-Bernoulli numbers and polynomials with weight 0,” Abstract and Applied Analysis, vol. 2011, Article ID 361484, 8 pages, 2011. View at Publisher · View at Google Scholar
  7. T. Kim, “On a q-analogue of the p-adic log gamma functions and related integrals,” Journal of Number Theory, vol. 76, no. 2, pp. 320–329, 1999. View at Publisher · View at Google Scholar
  8. T. Kim and J. Choi, “On the q-Euler numbers and polynomials with weight 0,” Applied Analysis, vol. 2012, Article ID 795304, 7 pages, 2012. View at Publisher · View at Google Scholar
  9. T. Kim, “On the q-extension of Euler and Genocchi numbers,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1458–1465, 2007. View at Publisher · View at Google Scholar
  10. T. Kim, “On the multiple q-Genocchi and Euler numbers,” Russian Journal of Mathematical Physics, vol. 15, no. 4, pp. 481–486, 2008. View at Publisher · View at Google Scholar
  11. T. Kim, “On the weighted q-Bernoulli numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 21, no. 2, pp. 207–215, 2011. View at Google Scholar
  12. T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288–299, 2002. View at Google Scholar · View at Zentralblatt MATH
  13. T. Kim, “q-Euler numbers and polynomials associated with p-adic q-integrals,” Journal of Nonlinear Mathematical Physics, vol. 14, no. 1, pp. 15–27, 2007. View at Publisher · View at Google Scholar
  14. T. Kim, “New approach to q-Euler polynomials of higher order,” Russian Journal of Mathematical Physics, vol. 17, no. 2, pp. 218–225, 2010. View at Publisher · View at Google Scholar
  15. T. Kim, “Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on p,” Russian Journal of Mathematical Physics, vol. 16, no. 4, pp. 484–491, 2009. View at Publisher · View at Google Scholar
  16. D. Kim, T. Kim, J. Choi, and Y.-H. Kim, “Identities involving q-Bernoulli and q-Euler numbers,” Abstract and Applied Analysis, vol. 2012, Article ID 674210, 10 pages, 2012. View at Publisher · View at Google Scholar
  17. C. S. Ryoo, “A note on the weighted q-Euler numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 21, pp. 47–54, 2011. View at Google Scholar