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arXiv · 1104.4721

Rational approximants for the Euler-Gompertz constant

Vasily Bolbachan
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Abstract

We obtain two sequences of rational numbers which converge to the Euler-Gompertz constant. Denote by the integral of f(x)e^{-x} from 0 to infinity. Recall that the Euler-Gompertz constant \delta is . Main idea. Let P_n(x) be a polynomial with integer coefficients. It is easy to prove that =a_n+ b_n$ for some integers a_n, b_n. Hence if /b_n converges to zero, a_n/b_n converges to - \delta . Main Theorem. Let u be positive real. There exists polynomials P_n(x)(they are explicitly given in the paper) such that tends to u as n tends to infinity. Proof of Main Theorem is elementary.

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Vasily Bolbachan. 2011-04-25. Rational approximants for the Euler-Gompertz constant. https://arxiv.org/abs/1104.4721

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