Quadratic and cubic harmonic number sums. (English) Zbl 1349.11053
Summary: This paper develops an approach to evaluation of Euler related sums. The approach is based on simple integral computations. By the approach, we can obtain some closed form representations of sums of quadratic and cubic harmonic numbers and reciprocal binomial coefficients. The given representations are new.
MSC:
| 11B75 | Other combinatorial number theory |
| 11M06 | \(\zeta (s)\) and \(L(s, \chi)\) |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 33C20 | Generalized hypergeometric series, \({}_pF_q\) |
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