Some evaluation of harmonic number sums |
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Authors: | Ce Xu Mingyu Zhang Weixia Zhu |
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Affiliation: | 1. School of Mathematical Sciences, Xiamen University, Xiamen, People's Republic of China15959259051@163.com;3. School of Mathematical Sciences, Xiamen University, Xiamen, People's Republic of China |
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Abstract: | In this paper, by using the method of partial fraction decomposition and integral representations of series, we establish some expressions of series involving harmonic numbers and binomial coefficients in terms of zeta values and harmonic numbers. Furthermore, we can obtain some closed form representations of sums of products of quadratic (or cubic) harmonic numbers and reciprocal binomial coefficients, and some explicit evaluations are given as applications. The given representations are new. |
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Keywords: | Polylogarithm function Euler sum Riemann zeta function harmonic number |
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