Department of Mathematics and Statistics,
York University, 4700 Keele St, Toronto,
ON M3J 1P3,
Canada.
E-mail: jmaxwellcampbell@gmail.com

Department of Mathematics, University of Taipei,
  No. 1, Ai-Guo West Road,
Taipei 10048, Taiwan.
E-mail: kwchen@uTaipei.edu.tw
URL: https://math.utaipei.edu.tw/p/412-1082-22.php

Abstract:

The modified Abel lemma on summation by parts has been applied in many ways recently to determine closed-form evaluations for infinite series involving generalized harmonic numbers with an upper parameter of two. We build upon such results using an integration technique that we apply to ``convert'' a given evaluation for such a series into an evaluation for a corresponding series involving squared harmonic numbers.

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