Summation of Harmonic Numbers

  • Dominic Y. Savio
  • Edmund A. Lamagna
  • Shing-Min Liu


The problem of finding closed forms for a summation involving harmonic numbers is considered. Solutions for ∑ i n =1P(i)H i (k) , where p(i) is a polynomial, and ∑ i n =1 Hi/(i+m), where m is an integer, are given. A method to automate these results is presented. This is achieved by using Moenck’s algorithm and by exploiting the relationship between polygamma functions and harmonic numbers.


Rational Function Closed Form Harmonic Number Finite Term Polygamma Function 
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.


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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Dominic Y. Savio
    • 1
  • Edmund A. Lamagna
    • 1
  • Shing-Min Liu
    • 1
  1. 1.Department of Computer Science and StatisticsThe University of Rhode IslandKingstonUSA

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