Approximations to Euler's constant

Details Approximations to Euler's constant Approximations to Euler's constant

2007-08-21

arxiv.org/abs/0708.2771v1

Mathematics

Number Theory

11 pages

Scientific paper

We study a problem of finding good approximations to Euler's constant $\gamma=\lim_{n\to\infty}S_n,$ where $S_n=\sum_{k=1}^n\frac{1}{n}-\log(n+1),$ by linear forms in logarithms and harmonic numbers. In 1995, C. Elsner showed that slow convergence of the sequence $S_n$ can be significantly improved if $S_n$ is replaced by linear combinations of $S_n$ with integer coefficients. In this paper, considering more general linear transformations of the sequence $S_n$ we establish new accelerating convergence formulae for $\gamma.$ Our estimates sharpen and generalize recent Elsner's, Rivoal's and author's results.

Affiliated with

Also associated with

No associations

Rating

Approximations to Euler's constant does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Approximations to Euler's constant, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximations to Euler's constant will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-366810