Skip to main content
Log in

A note on poly-Bernoulli and higher-order poly-Bernoulli polynomials

  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

In this paper, we consider poly-Bernoulli and higher-order poly-Bernoulli polynomials and derive some new and interesting identities of those polynomials by using umbral calculus.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Araci and M. Acikgoz, “A Note on the Frobenius-Euler Numbers and Polynomials Associated with Bernstein Polynomials,” Adv. Stud. Contemp. Math. (Kyungshang) 22(3), 399–406 (2012).

    MATH  MathSciNet  Google Scholar 

  2. D. Ding and J. Yang, “Some Identities Related to the Apostol-Euler and Apostol-Bernoulli Polynomials,” Adv. Stud. Contemp. Math. (Kyungshang) 20(1), 7–21 (2010).

    MATH  MathSciNet  Google Scholar 

  3. S. Gaboury, R. Tremblay, and B.-J. Fugère, “Some Explicit Formulas for Certain New Classes of Bernoulli, Euler and Genocchi Polynomials,” Proc. Jangjeon Math. Soc. 17(1), 115–123 (2014).

    MATH  MathSciNet  Google Scholar 

  4. M. Kaneko, “Poly-Bernoulli Numbers,” J. Théor. Nombres Bordeaux 9(1), 221–228 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  5. D. S. Kim and T. Kim, “Higher-Order Cauchy of the Second Kind and Poly-Cauchy of the Second Kind Mixed Type Polynomials,” Ars Combin. 115, 435–451 (2014).

    MathSciNet  Google Scholar 

  6. D. S. Kim, T. Kim, and S.-H. Lee, “A Note on Poly-Bernoulli Polynomials Arising from Umbral Calculus,” Adv. Stud. Theor. Phys. 7(15), 731–744 (2013).

    Google Scholar 

  7. T. Kim, H. I. Kwon, S.-H. Lee, and J.-J. Seo, “A Note on Poly-Bernoulli Numbers and Polynomials of the Second Kind,” Adv. Differen. Equations 2014, 2014:219.

    Article  Google Scholar 

  8. T. Kim, “Some Identities for the Bernoulli, the Euler and the Genocchi Numbers and Polynomials,” Adv. Stud. Contemp. Math. (Kyungshang) 20(1), 23–28 (2010).

    MATH  MathSciNet  Google Scholar 

  9. T. Kim, “Identities Involving Laguerre Polynomials Derived from Umbral Calculus,” Russ. J. Math. Phys. 21(1), 36–45 (2014).

    Article  MathSciNet  Google Scholar 

  10. S. Roman, The Umbral Calculus (Pure and Applied Mathematics, vol. 111, Academic Press, Inc. Harcourt Brace Jovanovich, Publishers, New York, 1984).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. Kim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, D., Kim, T. A note on poly-Bernoulli and higher-order poly-Bernoulli polynomials. Russ. J. Math. Phys. 22, 26–33 (2015). https://doi.org/10.1134/S1061920815010057

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920815010057

Keywords

Navigation