Rational approximations of values of the Gamma function on rationals

DOI10.1016/j.jnt.2009.08.003zbMath1206.11095OpenAlexW1992789048MaRDI QIDQ962996

Tanguy Rivoal

Publication date: 8 April 2010

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2009.08.003

zbMATH Keywords

Padé approximationEuler Gamma functionRational Diophantine approximationTernary linear recurrence sequences

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Transcendence theory of other special functions (11J91)

Related Items (7)

On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant ⋮ Polynomial continued fractions for exp(π) ⋮ Rational approximations for the quotient of gamma values ⋮ Values of the beta function: from Ramanujan's continued fraction to Hermite-Padé approximants ⋮ Rational approximations to values of the digamma function and a conjecture on denominators ⋮ Arithmetic theory of \(E\)-operators ⋮ Euler’s constant: Euler’s work and modern developments

Uses Software

• MultInt

Cites Work

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• Analytic theory of singular difference equations
• MultInt, a MAPLE package for multiple integration by the WZ method
• Rational approximations for values of derivatives of the Gamma function
• Modular functions and transcendence questions
• Multiple orthogonal polynomials for classical weights
• Applications of a theorem by A. B. Shidlovski

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