Analysis Mathematica

, 37:51 | Cite as

Summation formula involving harmonic numbers

  • Anthony SofoEmail author


Some identities of sums associated with harmonic numbers and binomial coefficients are developed. Integral representations and closed form identities of these sums are also given.


Zeta Function Series Representation Summation Formula Harmonic Number Wolfram Research 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

QFормула суммирования с гармоническими числами


QPолучены некоторые тождества для сумм, свяэанных с гармоническими числами и биномиальными коЭффициентами. QPолучены также интегральные представления и тождества в эамкнутои форме для таких сумм.


  1. [1]
    G. Almkvist, C. Krattenthaler, and J. Petersson, Some new formulas for π, Experiment. Math., 12(2003), 441–456.zbMATHMathSciNetGoogle Scholar
  2. [2]
    H. Alzer and S. Koumandos, Series representations for γ and other mathematical constants, Analysis Math., 34(2008), 1–8.CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    H. Alzer, D. Karaannakis, and H. M. Srivastava, Series representations of some mathematical constants, J. Math. Anal. Appl., 320(2006), 145–162.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    A. Basu, A new method in the study of Euler sums, Ramanujan J., 16(2008), 7–24.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    D. Borwein, J. Borwein, and R. Girgensohn, Explicit evaluation of Euler sums, Proc. Edinburgh Math. Soc., 38(2)(1995), 277–294.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    L. Euler, Opera Omnia, Ser. 1, Vol XV, Teubner (Berlin, 1917).Google Scholar
  7. [7]
    P. Flajolet and B. Salvy, Euler sums and contour integral representations, Exp. Math., 7(1998), 15–35.zbMATHMathSciNetGoogle Scholar
  8. [8]
    W. Janous, Around Apery’s constant, J. Inequal. Pure Appl. Math., 7(2006), article 35.Google Scholar
  9. [9]
    C. Krattenthaler and K. S. Rao, Automatic generation of hypergeometric identities by the beta integral method, J. Comput. Math. Appl., 160(2003), 159–173.CrossRefzbMATHGoogle Scholar
  10. [10]
    N. Nielsen, Die Gammafunktion, Chelsea (New York, 1965).Google Scholar
  11. [11]
    A. Sofo, Integral forms of sums associated with harmonic numbers, Appl. Math. Comput., 207(2009), 365–372.CrossRefzbMATHGoogle Scholar
  12. [12]
    A. Sofo, Computational Techniques for the Summation of Series, Kluwer Academic/Plenum Publishers (New York, 2003).zbMATHGoogle Scholar
  13. [13]
    A. Sofo, Sums of derivatives of binomial coefficients, Advances Appl. Math., 42(2009), 123–134.CrossRefzbMATHMathSciNetGoogle Scholar
  14. [14]
    A. Sofo, Harmonic numbers and double binomial coefficients, Integral Transforms and Spec. Funct., 20(11)(2009), 847–857.CrossRefzbMATHMathSciNetGoogle Scholar
  15. [15]
    J. Sondow and E.W. Weisstein, Harmonic number, MathWorld-A Wolfram Web Rescources,
  16. [16]
    H. M. Srivastava and J. Choi. Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers (Dordrecht-Boston, 2001).zbMATHGoogle Scholar
  17. [17]
    Wolfram Research Inc., Mathematica, Wolfram Research Inc., Champaign, IL.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.School of Engineering and ScienceVictoria UniversityMelbourne CityAustralia

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