On linear forms containing the Euler constant
Number Theory
2009-02-28 v2 Classical Analysis and ODEs
Abstract
We present linear forms with integer coefficients containing the Euler-Mascheroni and Euler-Gompertz constants. The forms are defined by four-terms recurrence relations. Asymptotics of the forms and their coefficients are obtained.
Cite
@article{arxiv.0902.1768,
title = {On linear forms containing the Euler constant},
author = {A. I. Aptekarev},
journal= {arXiv preprint arXiv:0902.1768},
year = {2009}
}
Comments
6 pages, second version -> some comments are added -> concerning implication of the fact - that one of two Euler-Mascheroni or Euler-Gompertz constants is an irratational number - from the Shidlovski theorem on algebraic independence of values of E-functions. This implication was indicated to the author by Yu. Nesterenko and T. Rivoal