Skip to main content
SpringerLink
Log in

New properties of r-Stirling series

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

The summation of some series involving the Stirling numbers of the first kind can be found in several works but there is no such a computation for Stirling numbers of the second kind let alone the r-Stirlings. We offer a comprehensive survey and prove new results.

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. V. Adamchik, On Stirling numbers and Euler sums, J. Comp. Appl. Math., 79 (1997), 119–130.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. T. Benjamin, D. Gaebler and R. Gaebler, A combinatorial approach to hyperharmonic numbers, INTEGERS: The Electornic Journal of Combinatorial Number Theory, 3 (2003), 1–9, # A15.

    MathSciNet  Google Scholar 

  3. D. Borwein and J. M. Borwein, On an intriguing integral and some series related to ζ(4), Proc. Amer. Math. Soc., 123 (1995), 1191–1198.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Z. Broder, The r-Stirling numbers, Disc. Math., 49 (1984), 241–259.

    Article  MATH  MathSciNet  Google Scholar 

  5. C. B. Corcino, L. C. Hsu and E. L. Tan, Asymptotic approximations of r-Stirling numbers, Approx. Theory and its Appl., 15 (1999), 13–25.

    MATH  MathSciNet  Google Scholar 

  6. R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison Wesley (1993).

  7. D. B. Grünberg, On asymptotics, Stirling numbers, gamma function and polylogs, Result. Math., 49 (2006), 89–125.

    Article  MATH  Google Scholar 

  8. H-K. Hwang, Asymptotic expansions for the Stirling numbers of the first kind, J. Comb. Theory, Ser. A., 71 (1998), 911–919.

    Google Scholar 

  9. A. D. Korshunov, Asymptotic behaviour of Stirling numbers of the second kind, Diskret. Analiz., 39 (1983), 24–41.

    MATH  MathSciNet  Google Scholar 

  10. K. S. Kölbig, Nielsen’s generalized polylogarithms, SIAM J. Math. Anal., 17, 1232–1256.

  11. I. Mező, Summation of hyperharmonic series, Publ. Math. Debrecen (submitted).

  12. I. Mező, Analytic extension of hyperharmonic numbers (manuscript).

  13. L. Moser and M. Wyman, Asymptotic development of the Stirling numbers of the first kind, J. London Math. Soc., 33 (1958), 133–146.

    Article  MATH  MathSciNet  Google Scholar 

  14. N. Nielsen, Der Eulerische Dilogarithmus und seine Verallgemeinerungen, Nova Acta Leopoldine, 90 (1909), 123–211.

    Google Scholar 

  15. N. M. Temme, Asymptotic estimates of Stirling numbers, Stud. Appl. Math., 89 (1993), 233–243.

    MATH  MathSciNet  Google Scholar 

  16. A. N. Timashev, On asymptotic expansions of Stirling numbers of the first and second kinds, Diskret. Mat., 10 (1998), 148–159.

    MathSciNet  Google Scholar 

  17. H. Wilf, The asymptotic behavior of the stirling numbers of the first kind, J. Comb. Theory, Ser. A., 64 (1993), 344–349.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Debrecen, Hungary

    I. Mező

Authors
  1. I. Mező
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Mező.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mező, I. New properties of r-Stirling series. Acta Math Hung 119, 341–358 (2008). https://doi.org/10.1007/s10474-007-7047-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-007-7047-9

Key words and phrases

2000 Mathematics Subject Classification

Search

Navigation