About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 584643, 11 pages
http://dx.doi.org/10.1155/2012/584643
Research Article

Some Identities on Bernoulli and Hermite Polynomials Associated with Jacobi Polynomials

1Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2Department of Mathematics, Sogang University, Seoul, Republic of Korea
3Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 17 July 2012; Accepted 9 August 2012

Academic Editor: Josef Diblík

Copyright © 2012 Taekyun 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. L. Carlitz, “The generating function for the Jacobi polynomial,” Rendiconti del Seminario Matematico della Università di Padova, vol. 38, pp. 86–88, 1967. View at Zentralblatt MATH
  2. L. Carlitz, “An integral formula for the Jacobi polynomial,” Bollettino dell'Unione Matematica Italiana, vol. 17, no. 3, pp. 273–275, 1962. View at Zentralblatt MATH
  3. L. Carlitz, “Some generating functions for the Jacobi polynomials,” Bollettino dell'Unione Matematica Italiana, vol. 16, no. 2, pp. 150–155, 1961. View at Zentralblatt MATH
  4. L. Carlitz, “On Laguerre and Jacobi polynomials,” Bollettino dell'Unione Matematica Italiana, vol. 12, no. 1, pp. 34–40, 1957. View at Zentralblatt MATH
  5. T. Kim, “On the weighted q-Bernoulli numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 21, no. 2, pp. 207–215, 2011.
  6. T. Kim, “An identity of the symmetry for the Frobenius-Euler polynomials associated with the Fermionic p-adic invariant q-integrals on p,” The Rocky Mountain Journal of Mathematics, vol. 41, no. 1, pp. 239–247, 2011. View at Publisher · View at Google Scholar
  7. 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
  8. T. Kim, “Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on p,” Russian Journal of Mathematical Physics, vol. 16, no. 1, pp. 93–96, 2009. View at Publisher · View at Google Scholar
  9. T. Kim, “On Euler-Barnes multiple zeta functions,” Russian Journal of Mathematical Physics, vol. 10, no. 3, pp. 261–267, 2003. View at Zentralblatt MATH
  10. T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288–299, 2002. View at Zentralblatt MATH
  11. H. Ozden, I. N. Cangul, and Y. Simsek, “Remarks on q-Bernoulli numbers associated with Daehee numbers,” Advanced Studies in Contemporary Mathematics, vol. 18, no. 1, pp. 41–48, 2009.
  12. H. Ozden, I. N. Cangul, and Y. Simsek, “Multivariate interpolation functions of higher-order q-Euler numbers and their applications,” Abstract and Applied Analysis, vol. 2008, Article ID 390857, 16 pages, 2008. View at Publisher · View at Google Scholar
  13. C. S. Ryoo, “A note on the Frobenius-Euler polynomials,” Proceedings of the Jangjeon Mathematical Society, vol. 14, no. 4, pp. 495–501, 2011.
  14. 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.
  15. 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.
  16. S.-H. Rim and S.-J. Lee, “Some identities on the twisted (h,q)-Genocchi numbers and polynomials associated with q-Bernstein polynomials,” International Journal of Mathematics and Mathematical Sciences, vol. 2011, Article ID 482840, 8 pages, 2011. View at Publisher · View at Google Scholar
  17. S.-H. Rim, E.-J. Moon, J.-H. Jin, and S.-J. Lee, “On the symmetric properties for the generalized Genocchi polynomials,” Journal of Computational Analysis and Applications, vol. 13, no. 7, pp. 1240–1245, 2011.
  18. S.-H. Rim, J.-H. Jin, E.-J. Moon, and S.-J. Lee, “Some identities on the q-Genocchi polynomials of higher-order and q-Stirling numbers by the fermionic p-adic integral on p,” International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 860280, 14 pages, 2010. View at Publisher · View at Google Scholar
  19. Y. Simsek, “Generating functions of the twisted Bernoulli numbers and polynomials associated with their interpolation functions,” Advanced Studies in Contemporary Mathematics, vol. 16, no. 2, pp. 251–278, 2008. View at Zentralblatt MATH
  20. Y. Simsek, “Special functions related to Dedekind-type DC-sums and their applications,” Russian Journal of Mathematical Physics, vol. 17, no. 4, pp. 495–508, 2010. View at Publisher · View at Google Scholar
  21. Y. Simsek and M. Acikgoz, “A new generating function of (q-) Bernstein-type polynomials and their interpolation function,” Abstract and Applied Analysis, vol. 2010, Article ID 769095, 12 pages, 2010. View at Publisher · View at Google Scholar
  22. Z. Zhang and H. Yang, “Some closed formulas for generalized Bernoulli-Euler numbers and polynomials,” Proceedings of the Jangjeon Mathematical Society, vol. 11, no. 2, pp. 191–198, 2008. View at Zentralblatt MATH
  23. W. A. Al-Salam and L. Carlitz, “Finite summation formulas and congruences for Legendre and Jacobi polynomials,” vol. 62, pp. 108–118, 1958. View at Zentralblatt MATH
  24. L. N. Karmazina, Tables of Jacobi Polynomials, Izdat. Akademii Nauk SSSR, Moscow, Russia, 1954.
  25. A. Bayad, “Modular properties of elliptic Bernoulli and Euler functions,” Advanced Studies in Contemporary Mathematics, vol. 20, no. 3, pp. 389–401, 2010.
  26. 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 Zentralblatt MATH
  27. 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
  28. I. N. Cangul, V. Kurt, H. Ozden, and Y. Simsek, “On the higher-order w-q-Genocchi numbers,” Advanced Studies in Contemporary Mathematics, vol. 19, no. 1, pp. 39–57, 2009.
  29. M. Can, M. Cenkci, V. Kurt, and Y. Simsek, “Twisted Dedekind type sums associated with Barnes' type multiple Frobenius-Euler l-functions,” Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 135–160, 2009.