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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive
Teor. Veroyatnost. i Primenen., 2021 Volume 66, Issue 1, Pages 110–128 (Mi tvp5319)
This article is cited in 1 paper

An estimate for the sum of the Spitzer series and its generalization

S. V. Nagaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: An upper estimate for the absolute value of the sum of the Spitzer series is obtained. This estimate depends explicitly on the distribution in terms of which the Spitzer series is defined.

Keywords: zeta function, expectation, normal law, Berry–Esseen estimate, Euler constant, Spitzer series.

Received: 18.05.2019
Revised: 07.09.2020
Accepted: 17.09.2020

DOI: 10.4213/tvp5319


 English version: Theory of Probability and its Applications, 2021, 66:1, 89–104

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© Steklov Math. Inst. of RAS, 2025