Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 760613, 7 pages
http://dx.doi.org/10.1155/2014/760613
Research Article

Some New Formulae for Genocchi Numbers and Polynomials Involving Bernoulli and Euler Polynomials

1Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, 27410 Gaziantep, Turkey
2Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaziantep, Turkey
3Department of Mathematics, Faculty of Science and Letters, Namik Kemal University, 59030 Tekirdağ, Turkey
4Department of Mathematics Engineering, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

Received 9 January 2014; Accepted 26 March 2014; Published 24 April 2014

Academic Editor: Ram N. Mohapatra

Copyright © 2014 Serkan Araci 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. S. Araci, “Novel identities for q-Genocchi numbers and polynomials,” Journal of Function Spaces and Applications, vol. 2012, Article ID 214961, 13 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  2. S. Araci, “Novel identities involving Genocchi numbers and polynomials arising from applications from umbral calculus,” Applied Mathematics and Computation, vol. 233, pp. 599–607, 2014. View at Google Scholar
  3. S. Araci, E. Şen, and M. Acikgoz, “Theorems on Genocchi polynomials of higher order arising from Genocchi basis,” Taiwanese Jouurnal of Mathematics, vol. 18, no. 2, pp. 473–482, 2014. View at Publisher · View at Google Scholar
  4. S. Araci, M. acikgoz, A. Bagdasaryan, and E. Şen, “The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials,” Turkish Journal of Analysis and Number Theory, vol. 1, no. 1, pp. 1–3, 2013. View at Google Scholar
  5. S. Araci, M. Acikgoz, and E. Şen, “On the extended Kim's p-adic q-deformed fermionic integrals in the p-adic integer ring,” Journal of Number Theory, vol. 133, no. 10, pp. 3348–3361, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  6. T. Kim, “Some identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 20, no. 1, pp. 23–28, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. Genocchi, “Intorno all' espressione generale de' Numeri Bernulliani,” Annali Di SciEnzE MatEmatichE E FisichE, vol. 3, pp. 395–405, 1852. View at Google Scholar
  8. A. F. Horadam, “Genocchi polynomials,” in Proceedings of the 4th International Conference on Fibonacci Numbers and Their Applications, pp. 145–166, Kluwer Academic, 1991.
  9. A. F. Horadam, “Negative order Genocchi polynomials,” The Fibonacci Quarterly, vol. 30, no. 1, pp. 21–34, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. M. Srivastava, B. Kurt, and Y. Simsek, “Some families of Genocchi type polynomials and their interpolation functions,” Integral Transforms and Special Functions, vol. 23, no. 12, pp. 919–938, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. H. M. Srivastava, “Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials,” Applied Mathematics & Information Sciences, vol. 5, no. 3, pp. 390–444, 2011. View at Google Scholar · View at MathSciNet
  12. 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 · View at MathSciNet
  13. D. S. Kim, T. Kim, S. H. Lee, and Y. H. Kim, “Some identities for the product of two Bernoulli and Euler polynomials,” Advances in Difference Equations, vol. 2012, article 95, 2012. View at Google Scholar
  14. D. S. Kim, D. V. Dolgy, T. Kim, and S.-H. Rim, “Some formulae for the product of two Bernoulli and Euler polynomials,” Abstract and Applied Analysis, vol. 2012, Article ID 784307, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. S. Kim and T. Kim, “Bernoulli basis and the product of several Bernoulli polynomials,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 463659, 12 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. V. Gupta, T. Kim, J. Choi, and Y. H. Kim, “Generating functions for g-Bernstein, g-Meyer-König-Zeller and g-Beta basis,” Automation, Computers, Applied Mathematics, vol. 19, no. 1, pp. 7–11, 2010. View at Google Scholar
  17. L. Carlitz, “Multiplication formulas for products of Bernoulli and Euler polynomials,” Pacific Journal of Mathematics, vol. 9, pp. 661–666, 1959. View at Publisher · View at Google Scholar · View at MathSciNet
  18. L. Carlitz, “The product of two Eulerian polynomials,” Mathematics Magazine, vol. 36, no. 1, pp. 37–41, 1963. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001. View at MathSciNet
  20. K.-W. Chen, “Sums of products of generalized Bernoulli polynomials,” Pacific Journal of Mathematics, vol. 208, no. 1, pp. 39–52, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. F. Qi, “Explicit formulas for computing Euler polynomials in terms of the second kind Stirling numbers,” http://arxiv.org/abs/1310.5921.
  22. F. Qi, “Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind,” Filomat, vol. 28, pp. 1–9, 2014. View at Google Scholar
  23. B.-N. Guo and F. Qi, “Some identities and an explicit formula for Bernoulli and Stirling numbers,” Journal of Computational and Applied Mathematics, vol. 255, pp. 568–579, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  24. Y. He and C. Wang, “Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 927953, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. S.-H. Rim and J. Jeong, “On the modified q-Euler numbers of higher order with weight,” Advanced Studies in Contemporary Mathematics, vol. 22, no. 1, pp. 93–98, 2012. View at Google Scholar · View at MathSciNet