## versión On-line ISSN 0719-0646

### Cubo vol.15 no.3 Temuco  2013

#### http://dx.doi.org/10.4067/S0719-06462013000300010

Euler's constant, new classes of sequences and estimates

Alina Sîntămărian

Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania. alina.sintamarian@math.utcluj.ro

ABSTRACT

We give two classes of sequences with the argument of the logarithmic term modified and also with some additional terms besides those in the denition sequence, and that converge quickly to , where a (0, + ). We present the pattern in forming these sequences, expressing the coefficients that appear with the Bernoulli numbers. Also, we obtain estimates containing best constants for and , where = (1) is the Euler's onstant.

Keywords and Phrases: sequence, convergence, approximation, Euler's constant, Bernoulli number, estimate.

RESUMEN

Mostramos dos clases de secuencias con el argumento del término logarítmico modificado y también con algunos términos adicionales además de los definidos en la secuencia y que convergen rápidamente a , donde a (0, + ). Presentamos el patrón que forma las secuencias expresando los coefientes que aparecen en los números de Bernoulli. Además, obtenemos estimaciones que contienen las mejores constantes para y , donde = (1) es la constante de Euler.

2010 AMS Mathematics Subject Classification: 11Y60, 11B68, 40A05, 41A44, 33B15.

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Received: September 2012 / Accepted: September 2013.

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