Published by De Gruyter (O) January 14, 2013

New sequences that converge to a generalized Euler constant

Alina Sîntămărian

From the journal Analysis

https://doi.org/10.1524/anly.2012.1153

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Abstract

The purpose of the paper is to give some sequences that converge quickly to a generalized Euler constant, i.e. the limit of the sequence

(1/a^s+1/(a+1)^s+⋯+1/(a+n-1)^s-1/(1-s)((a+n-1)^1-s-a^1-s))_n ∈ ℕ,

where a ∈ (0,+∞) and s ∈ (0,1).

Keywords: sequence (11B50); convergence (40A05); approximation (41A60); generalized Euler constant (11Y60); Ioachimescu's constant (11Y60)

^* Correspondence address: Technical University of Cluj-Napoca, Department of Mathematics, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Rumänien, Alina.Sintamarian@math.utcluj.ro

Published Online: 2013-01-14

Published in Print: 2012-06

New sequences that converge to a generalized Euler constant

Abstract

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