Abstract
Introduction/purpose: Some sums of the polylogarithmic function associated with harmonic numbers are established. Methods: The approach is based on using the summation methods. Results: This paper generalizes the results of the zeta function series associated with the harmonic numbers. Conclusions: Various interesting series as the consequence of the generalization are obtained.
Highlights
Introduction and preliminariesThe polylogarithm is a function in mathematics which was investigated intensively by many mathematicians
To assure the accuracy of the results, we verified all the numerical series identities through Wolfram Alpha
Further questions can be asked regarding the sums with harmonic numbers of an arbitrary order as to, whether it is possible to find more of them of the form H n for some fixed k. k
Summary
Introduction and preliminariesThe polylogarithm is a function in mathematics which was investigated intensively by many mathematicians. 1 0 dt Li(s−1)(z)−z−(Li(s−1)(zt)−zt) m)2 (z m)−z m−(Li(s−1) 1−r (z mr)−zmr) The corollaries of the results are given as follows. The following equalities come from Theorem 3.
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