Abstract
We present a new integration method for evaluating infinite series involving alternating harmonic numbers. Using this technique, we provide new evaluations for series containing factors of the form \(\left( {\begin{array}{c}2n\\ n\end{array}}\right) ^{2} H_{2n}'\) that cannot be evaluated using known generating functions involving harmonic-type numbers. A closed-form evaluation is given for the series:
and we show how the integration method given in our article may be applied to evaluate natural generalizations and variants of the above series, such as the binomial-harmonic series:
introduced in our article.
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Campbell, J.M. Series Containing Squared Central Binomial Coefficients and Alternating Harmonic Numbers. Mediterr. J. Math. 16, 37 (2019). https://doi.org/10.1007/s00009-019-1311-4
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DOI: https://doi.org/10.1007/s00009-019-1311-4