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On Evaluations of Euler-type Sums of Hyperharmonic Numbers
- Publication Year :
- 2021
-
Abstract
- We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers $h_{n}^{\left( r\right) }$ with reciprocal binomial coefficients. These evaluations enable us to extend closed form formula of Euler sums of hyperharmonic numbers to an arbitrary integer $r$. Moreover, we reach at explicit formulas for the shifted Euler-type sums of harmonic and hyperharmonic numbers. All the evaluations are provided in terms of the Riemann zeta values, harmonic numbers and linear Euler sums.<br />Comment: 17 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2103.11876
- Document Type :
- Working Paper