Skip to main content
SpringerLink
Log in

Generalized incomplete poly-Bernoulli and poly-Cauchy numbers

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

By using the restricted and associated Stirling numbers of the first kind and by generalizing the (unsigned) Stirling numbers of the first kind, we define the generalized incomplete poly-Cauchy numbers by combining the generalized and the incomplete poly-Cauchy numbers, and study their arithmetical and combinatorial properties. We also study the corresponding generalized incomplete poly-Bernoulli numbers.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Cenkci, T. Komatsu, Poly-Bernoulli numbers and polynomials with a \(q\) parameter. J. Number Theory 152, 38–54 (2015)

    Article  MathSciNet  Google Scholar 

  2. C.A. Charalambides, Enumerative Combinatorics (Discrete Mathematics and Its Applications) (Chapman and Hall/CRC, London, 2002)

    Google Scholar 

  3. L. Comtet, Advanced Combinatorics (Reidel, Dordrecht, 1974)

    Book  MATH  Google Scholar 

  4. F.T. Howard, Associated Stirling numbers. Fibonacci Quart. 18, 303–315 (1980)

    MathSciNet  MATH  Google Scholar 

  5. Ch. Jordan, Calculus of Finite Differences (Chelsea Publ. Co., New York, 1950)

    MATH  Google Scholar 

  6. M. Kaneko, Poly-Bernoulli numbers. J. Th. Nombres Bordeaux 9, 221–228 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Komatsu, Poly-Cauchy numbers. Kyushu J. Math. 67, 143–153 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Komatsu, Poly-Cauchy numbers with a \(q\) parameter. Ramanujan J. 31, 353–371 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. T. Komatsu, Hypergeometric Cauchy numbers. Int. J. Number Theory 9, 545–560 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Komatsu, Incomplete poly-Cauchy numbers. Monatsh. Math. 180, 271–288 (2016)

  11. T. Komatsu, V. Laohakosol, K. Liptai, A generalization of poly-Cauchy numbers and their properties, Abstr. Appl. Anal. 2013(2013), Article ID 179841, 8 pages

  12. T. Komatsu, K. Liptai, I. Mező, Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers. Publ. Math. Debrecen 88, 357–368 (2016)

  13. T. Komatsu, I. Mező, L. Szalay, Incomplete Cauchy numbers. Acta Math. Hungar. 149, 306–323 (2016)

  14. T. Komatsu, L. Szalay, Shifted poly-Cauchy numbers. Lith. Math. J. 54, 166–181 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Merlini, R. Sprugnoli, M.C. Verri, The Cauchy numbers. Discret. Math. 306, 1906–1920 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. I. Mező, Periodicity of the last digits of some combinatorial sequences, J. Integer Seq. 17 (2014), Article 14.1.1

  17. J. Riordan, Combinatorial Identities (Wiley, New York, 1968)

    MATH  Google Scholar 

  18. Y. Sasaki, On generalized poly-Bernoulli numbers and related \(L\)-functions. J. Number Theory 132, 156–170 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. F.-Z. Zhao, Some properties of associated Stirling numbers, J. Integer Seq. 11 (2008), Article 08.1.7, 9 pages

Download references

Acknowledgements

The author was supported in part by the grant of Wuhan University and by the grant of Hubei Provincial Experts Program.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Takao Komatsu

Authors
  1. Takao Komatsu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takao Komatsu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Komatsu, T. Generalized incomplete poly-Bernoulli and poly-Cauchy numbers. Period Math Hung 75, 96–113 (2017). https://doi.org/10.1007/s10998-016-0167-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-016-0167-7

Keywords

Search

Navigation