Skip to main content
Log in

Generalized Bernoulli Polynomials and Numbers, Revisited

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

We describe with some new details the connection between generalized Bernoulli polynomials, Bernoulli polynomials and generalized Bernoulli numbers (Norlund polynomials). A new recursive and explicit formulae for these polynomials are derived.

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. Bretti, G., Natalini, P., Ricci, P.E.: Generalizations of the Bernoulli and Appel polynomials. Abstract Appl. Anal. 7, 613–623 (2004). doi:10.1155/S1085337504306263

  2. Burić T., Elezović N.: Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions. J. Comput. Appl. Math. 235, 3315–3331 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen C.-P., Elezović N., Vukšić L.: Asymptotic formulae associated with the Wallis power function and digamma function. J. Class. Anal. 2(2), 151–166 (2013)

    MathSciNet  Google Scholar 

  4. Dilcher K.: Sums of products of Bernoulli numbers. J. Number Theory 60(1), 23–41 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gessel I.M.: On Mikis identity for Bernoulli numbers. J. Number Theory 110, 75–82 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kim M.-S.: A note on sums of products of Bernoulli numbers. Appl. Math. Lett. 24(1), 55–61 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lu D.-Q.: Some properties of Bernoulli polynomials and their generalizations. Appl. Math. Lett. 24, 746–751 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Luke, Y.L.: The Special Functions and Their Approximations, Vol. I. Academic Press, New York (1969)

  9. Natalini, P., Bernardini, A.: Generalization of the Berboulli polynomials. J. Appl. Math. 3, 155–163 (2003). doi:10.1155/S1110757X03203101

  10. Srivastava H.M., Pintér Á.: Remarks on some relationships between the Bernoulli and Euler polynomials. Appl. Math. Lett. 17, 375–380 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tempesta P.: On Appell sequences of polynomials of Bernoulli and Euler type. J. Math. Anal. Appl. 341, 1295–1310 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Neven Elezović.

Additional information

This research is supported by Croatian Science Foundation under the project 5435.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Elezović, N. Generalized Bernoulli Polynomials and Numbers, Revisited. Mediterr. J. Math. 13, 141–151 (2016). https://doi.org/10.1007/s00009-014-0498-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-014-0498-7

Mathematical Subject Classification

Keywords

Navigation