Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415469 | Journal of Number Theory | 2015 | 9 Pages |
Abstract
The hyperharmonic numbers hn(r) are defined by means of the classical harmonic numbers. We show that the Euler-type sums with hyperharmonic numbers:Ï(r,m)=ân=1âhn(r)nm can be expressed in terms of series of Hurwitz zeta function values. This is a generalization of a result of MezÅ and Dil (2010) [7]. We also provide an explicit evaluation of Ï(r,m) in a closed form in terms of zeta values and Stirling numbers of the first kind. Furthermore, we evaluate several other series involving hyperharmonic numbers.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ayhan Dil, Khristo N. Boyadzhiev,