Advanced Studies in Contemporary Mathematics

Jangjeon Mathematical Society (장전수학회)
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NEW APPROACH TO q-BERNOULLI POLYNOMIALS WITH WEIGHT OR WEAK WEIGHT

  • Park, Jin-Woo (DEPARTMENT DE MATHEMATICS EDUCATION, KYUNGPOOK NATIONAL UNIVERSITY)
  • Published : 2014.01.01
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Abstract

In this paper, we construct new q-extension of Bernoulli polynomials with weight ${\alpha}$ or weak weight ${\beta}$. These q-Bernoulli poly-nomials are useful to study various identities of Carlita's q-Bernoulli numbers.

Keywords

References

  1. M. Acikoz, D. Erdal and S. Araci, A new approach to q-Bernoulli numbers and q-Bernoulli polynomials related to q-Bernstein polynomials, Adv. Differece Equ., 2010, Art. ID 951764, 9pp.
  2. A. Bayad and T. Kim, Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials, Russ. J. Math. Phys., 18 (2011), no. 2, 133-143. https://doi.org/10.1134/S1061920811020014
  3. L. Carlitz, q-Bernoulli and Eulerian numbers, Trans. Amer. Math. Soc., 76 (1954), 332-350.
  4. L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J., 15 (1948), 987-1000. https://doi.org/10.1215/S0012-7094-48-01588-9
  5. J. Choi and T. Kim, Arithmetic properties for the q-Bernoulli number's and polynomials, Proc. Jangjeon Math. Soc., 15 (2012), no. 2, 137-143.
  6. J. Choi, T. Kim and Y. H. Kim, A note on the extended q-Bernoulli numbers and polynomials, Adv. Stud. Contemp. Math., 21 (2011), no. 4, 351-354.
  7. T. Kim, On the weighted q-Bernoulli numbers and polynomials, Adv. Stud. Contemp. Math., 21 (2011), no. 2, 207-215.
  8. T. Kim, q-Bernoulli numbers and polynomials associated with Gaussian binomial co-efficients, Russ. J. Math. Phys., 15 (2008), no. 1, 51-57. https://doi.org/10.1134/S1061920808010068
  9. T. Kim, On q-analogye of the p-adic log gamma functions and related integral, J. Number Theory, 76 (1999), no. 2, 320-329. https://doi.org/10.1006/jnth.1999.2373
  10. T. Kim, q-Volkenborn integration, Russ. J. Math. Phys., 9 (2002), no. 3, 288-299.
  11. T. Kim, and J.Choi, On the a-Bernoulli number's and polynomials with weight ${\alpha}$, Abstr. Appl. Anal., 2011, Art. ID 392025, 14 pages.
  12. T. Kim, D. V. Dolgy, S. H. Lee, B. Lee and S. H. Rim, A note on the modified qBernoullii numbers and polynomials with weight ${\alpha}$., Abstr. Appl. Anal., 2011, Art. ID 545314, 8 pp.
  13. S. H. Rim, T. Kim and B. Lee, Some identities on the extended Carlitz's q-Bernoulli numbers and polynomials, J. Comput. Anal. Appl., 14 (2012), no. 3, 536-543.
  14. J. Seo, T. Kim and S. H. Rim, A note on the new approach to q-Bernoulli polynomials, Appl. Math. Sci, 7 (2013), no. 94, 4675-4680.
  15. Y. Simesk V, Kurt and D. Kim, New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials, Adv. Stud. Contemp. Math., 12 (2006), 237-246.