Rational approximations for the quotient of gamma values

Details Rational approximations for the quotient of gamma values Rational approximations for the quotient of gamma values

2010-10-03

arxiv.org/abs/1010.0429v2

Mathematics

Number Theory

15 pages; to appear in Indag. Math

Scientific paper

In this paper, we continue to study properties of rational approximations to Euler's constant and values of the Gamma function defined by linear recurrences, which were found recently by A. I. Aptekarev and T. Rivoal. Using multiple Jacobi-Laguerre orthogonal polynomials we present rational approximations to the quotient of values of the Gamma function at rational points. As a limit case of our result, we obtain new explicit formulas for numerators and denominators of the Aptekarev approximants to Euler's constant.

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