Summation of Harmonic Numbers
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.
KeywordsRational Function Closed Form Harmonic Number Finite Term Polygamma Function
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