Euler's constant, new classes of sequences and estimates

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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 definition sequence, and that converge quickly to , where  . 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 is the Euler's constant.

Keywords

sequence , convergence , approximation , Euler's constant , Bernoulli number , estimate
  • Alina Sîntamarian Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania.
  • Pages: 105-122
  • Date Published: 2013-10-01
  • Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal

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Published

2013-10-01

How to Cite

[1]
A. Sîntamarian, “Euler’s constant, new classes of sequences and estimates”, CUBO, vol. 15, no. 3, pp. 105–122, Oct. 2013.

Issue

Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal

Section

Articles