Rational approximants for the Euler-Gompertz constant

Details Rational approximants for the Euler-Gompertz constant Rational approximants for the Euler-Gompertz constant

2011-04-25

arxiv.org/abs/1104.4721v2

Mathematics

Number Theory

Added a references to MMCS; 16 pages

Scientific paper

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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