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Abstract and Applied Analysis
Volume 2011, Article ID 545314, 8 pages
http://dx.doi.org/10.1155/2011/545314
Research Article

A Note on the Modified -Bernoulli Numbers and Polynomials with Weight

1Division of General Education, Kwangwoon University, Seoul 139-701, Republic of Korea
2Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea
3Department of Wireless Communications Engineering, Kwangwoon University, Seoul 139-701, Republic of Korea
4Department of Mathematics Education, Kyungpook National University, Taegu 702-701, Republic of Korea

Received 13 July 2011; Accepted 2 October 2011

Academic Editor: Alberto d'Onofrio

Copyright © 2011 T. 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, “Expansions of q-Bernoulli numbers,” Duke Mathematical Journal, vol. 25, pp. 355–364, 1958. View at Publisher · View at Google Scholar
  2. L. Carlitz, “q-Bernoulli numbers and polynomials,” Duke Mathematical Journal, vol. 15, pp. 987–1000, 1948. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. 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
  4. 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
  5. T. Kim, “Non-Archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials,” Russian Journal of Mathematical Physics, vol. 10, no. 1, pp. 91–98, 2003. View at Google Scholar
  6. T. Kim, “q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients,” Russian Journal of Mathematical Physics, vol. 15, no. 1, pp. 51–57, 2008. View at Google Scholar · View at Zentralblatt MATH
  7. T. Kim, Y.-H. Kim, and B. Lee, “A note on Carlitz's q-Bernoulli measure,” Journal of Computational Analysis and Applications, vol. 13, no. 3, pp. 590–595, 2011. View at Google Scholar
  8. A. S. Hegazi and M. Mansour, “A note on q-Bernoulli numbers and polynomials,” Journal of Nonlinear Mathematical Physics, vol. 13, no. 1, pp. 9–18, 2006. View at Publisher · View at Google Scholar
  9. 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. View at Google Scholar
  10. 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
  11. 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
  12. 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