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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2025 Volume 65, Number 1, Pages 8–24 (Mi zvmmf11912)

Papers published in the English version of the journal

Product sums of zeta tails by series rearrangements

Chunli Lia, Wenchang Chub

a School of Mathematics and Statistics, Zhoukou Normal University, Henan, China
b Via Dalmazio Birago 9/E, 73100, Lecce, Italy

Abstract: Product sums of zeta like tails are examined by means of series rearrangements. Six classes of them are shown to be expressible in terms of Riemann’s zeta function, and Dirichlet’s eta, lambda and beta functions. Several remarkable closed formulae are established as consequences.

Key words: harmonic number, double Euler sums, Riemann zeta function.

Received: 24.02.2024
Revised: 10.09.2024
Accepted: 17.03.2025

Language: English


 English version:
Computational Mathematics and Mathematical Physics, 2025, 65:1, 8–24


© Steklov Math. Inst. of RAS, 2026