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Infinite Series Containing Generalized Harmonic Numbers

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Abstract

Applying the modified Abel lemma on summation by parts, we examine infinite series containing generalized harmonic numbers of order 2 and 3. Several interesting results mainly for \(\pi ^2\) and \(\zeta (3)\) are established as consequences.

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  1. School of Science, Dalian Jiaotong University, Dalian, 116028, People’s Republic of China

    Xiaoyuan Wang

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  1. Xiaoyuan Wang
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Correspondence to Xiaoyuan Wang.

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Wang, X. Infinite Series Containing Generalized Harmonic Numbers. Results Math 73, 24 (2018). https://doi.org/10.1007/s00025-018-0774-0

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  • DOI: https://doi.org/10.1007/s00025-018-0774-0

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