Alternating Euler $T$ -sums and Euler $\tilde S$ -sums

preprint2020arXivOpen access

In this paper, we study the alternating Euler $T$ -sums and related sums by using the method of contour integration. We establish the explicit formulas for all linear and quadratic Euler $T$ -sums and related sums. Some interesting new consequences and illustrative examples are considered.

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Alternating Euler $T$ -sums and Euler $\tilde S$ -sums

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Alternating Euler TTT-sums and Euler S~\tilde SS~-sums

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Alternating Euler $T$ -sums and Euler $\tilde S$ -sums