Rational approximations to values of the digamma function and a conjecture on denominators

DOI10.1134/S0001434611110113zbMath1282.11076OpenAlexW2024835304WikidataQ123024934 ScholiaQ123024934MaRDI QIDQ2435866

Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood

Publication date: 20 February 2014

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434611110113

zbMATH Keywords

Laguerre polynomialEuler gamma functiondigamma functionEuler constantPochhammer symbolhypergeometric sumAptekarev approximationrational approximation to a numberRivoal approximation

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Transcendence theory of other special functions (11J91) Simultaneous homogeneous approximation, linear forms (11J13)

Related Items (2)

On a continued fraction expansion for Euler's constant ⋮ Rational approximations for the quotient of gamma values

Uses Software

• MultiZeilberger

Cites Work

• Unnamed Item
• Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory
• Rational approximations of values of the Gamma function on rationals
• A system of recurrence relations for rational approximations of the Euler constant
• On the method of Thue-Siegel
• A new proof of the irrationality of \(\zeta (2)\) and \(\zeta (3)\) using Padé approximants
• Rational approximations for values of derivatives of the Gamma function
• Multiple orthogonal polynomials for classical weights

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