Results in Mathematics

, Volume 58, Issue 3–4, pp 329–335

A New Formula for the Bernoulli Polynomials

Article

Abstract

In this note we show that a seemingly new class of Stirling-type pairs can be applied to produce a new representation of the Bernoulli polynomials at positive rational arguments. A class of generalized harmonic numbers is also investigated, and we point out that these give a new relation for the so-called harmonic polynomials.

Mathematics Subject Classification (2010)

11B73 

Keywords

Stirling numbers r-Stirling numbers Whitney numbers Bernoulli polynomials Harmonic numbers Stirling-type pairs Hyperharmonic numbers Harmonic polynomials 

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References

  1. 1.
    Benjamin A.T., Gaebler D., Gaebler R.: A combinatorial approach to hyperharmonic numbers. INTEGERS Electron J Combin Number Theory 3, 1–9 (2003) #A15MathSciNetGoogle Scholar
  2. 2.
    Benoumhani M.: On Whitney numbers of Dowling lattices. Discrete Math. 159, 13–33 (1996)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Broder A.Z.: The r-Stirling numbers. Discrete Math. 49, 241–259 (1984)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cheon G.-S., El-Mikkawy M.E.A.: Generalized harmonic numbers with Riordan arrays. J. Number Theory 128(2), 413–425 (2008)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Dil A., Mező I.: A symmetric algorithm for hyperharmonic and Fibonacci numbers. Appl. Math. Comput. 206, 942–951 (2008)MATHMathSciNetGoogle Scholar
  6. 6.
    Hsu L.C., Shiue P.J.-S.: A unified approach to generalized Stirling numbers. Adv. Appl. Math. 20, 366–384 (1998)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Graham R.L., Knuth D.E., Patashnik O.: Concrete Mathematics. Addison- Wesley, Reading (1989)MATHGoogle Scholar
  8. 8.
    Mező I., Dil A.: Euler–Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence. Cent. Eur. J. Math. 7(2), 310–321 (2009)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Probability Theory, Faculty of InformaticsUniversity of DebrecenDebrecenHungary

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