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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 179385, 13 pages
http://dx.doi.org/10.1155/2012/179385
Research Article

Some Properties of Multiple Generalized q-Genocchi Polynomials with Weight and Weak Weight

Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea

Received 28 May 2012; Revised 21 August 2012; Accepted 22 August 2012

Academic Editor: Cheon Ryoo

Copyright © 2012 J. Y. Kang. 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. T. Kim, “New approach to q-Euler, Genocchi numbers and their interpolation functions,” Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009. View at Google Scholar
  2. T. Kim, “Note on the q-Euler numbers of higher order,” Advanced Studies in Contemporary Mathematics, vol. 19, no. 1, pp. 25–29, 2009. View at Google Scholar
  3. T. Kim, “The modified q-Euler numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 16, no. 2, pp. 161–170, 2008. View at Google Scholar
  4. 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
  5. T. Kim, “Barnes-type multiple q-zeta functions and q-Euler polynomials,” Journal of Physics A, vol. 43, no. 25, 11 pages, 2010. View at Publisher · View at Google Scholar
  6. 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
  7. T. Kim, J. Choi, Y. H. Kim, and C. S. Ryoo, “A note on the weighted p-adic q-Euler measure on p,” Advanced Studies in Contemporary Mathematics, vol. 21, no. 1, pp. 35–40, 2011. View at Google Scholar
  8. C. S. Ryoo, “Some identities of the twisted q-Euler numbers and polynomials associated with q-Bernstein polynomials,” Proceedings of the Jangjeon Mathematical Society, vol. 14, no. 2, pp. 239–248, 2011. View at Google Scholar
  9. C. S. Ryoo, “On the generalized Barnes type multiple q-Euler polynomials twisted by ramified roots of unity,” Proceedings of the Jangjeon Mathematical Society, vol. 13, no. 2, pp. 255–263, 2010. View at Google Scholar
  10. C. S. Ryoo, “Some relations between twisted q-Euler numbers and Bernstein polynomials,” Advanced Studies in Contemporary Mathematics, vol. 21, no. 2, pp. 217–223, 2011. View at Google Scholar
  11. C. S. Ryoo, “A numerical computation on the structure of the roots of q-extension of Genocchi polynomials,” Applied Mathematics Letters, vol. 21, no. 4, pp. 348–354, 2008. View at Publisher · View at Google Scholar
  12. C. S. Ryoo, T. Kim, J. Choi, and B. Lee, “On the generalized q-Genocchi numbers and polynomials of higher-order,” Advances in Difference Equations, vol. 2011, Article ID 424809, 8 pages, 2011. View at Google Scholar
  13. L.-C. Jang, “A study on the distribution of twisted q-Genocchi polynomials,” Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 181–189, 2009. View at Google Scholar
  14. L.-C. Jang, “On multiple generalized w-Genocchi polynomials and their applications,” Mathematical Problems in Engineering, vol. 2010, Article ID 316870, 8 pages, 2010. View at Publisher · View at Google Scholar
  15. A. Bayad and T. Kim, “Identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 20, no. 2, pp. 247–253, 2010. View at Google Scholar · View at Zentralblatt MATH
  16. A. Bayad and T. Kim, “Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials,” Russian Journal of Mathematical Physics, vol. 18, no. 2, pp. 133–143, 2011. View at Publisher · View at Google Scholar
  17. B. Kurt, “The multiplication formulae for the Genocchi polynomials,” Proceedings of the Jangjeon Mathematical Society, vol. 13, no. 1, pp. 89–96, 2010. View at Google Scholar · View at Zentralblatt MATH
  18. M. Cenkci, M. Can, and V. Kurt, “q-adic interpolation functions and Kummer-type congruences for q-twisted and q-generalized twisted Euler numbers,” Advanced Studies in Contemporary Mathematics, vol. 9, no. 2, pp. 203–216, 2004. View at Google Scholar
  19. M. Domaratzki, “Combinatorial interpretations of a generalization of the Genocchi numbers,” Journal of Integer Sequences, vol. 7, no. 3, article 04.3.6, 2004. View at Google Scholar · View at Zentralblatt MATH
  20. Y. Simsek, I. N. Cangul, V. Kurt, and D. Kim, “q-Genocchi numbers and polynomials associated with q-Genocchi-type l-functions,” Advances in Difference Equations, vol. 2008, Article ID 815750, 12 pages, 2008. View at Google Scholar
  21. D. V. Dolgy, T. Kim, B. Lee, and C. S. Ryoo, “On the q-analogue of Euler measure with weight α,” Advanced Studies in Contemporary Mathematics, vol. 21, no. 4, pp. 429–435, 2011. View at Google Scholar