Type II Hermite-Padé approximations of generalized hypergeometric series

DOI10.1007/s00365-010-9111-xzbMath1236.41017OpenAlexW2051510097MaRDI QIDQ658981

Tapani Matala-aho

Publication date: 9 February 2012

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-010-9111-x

zbMATH Keywords

Padé approximationhypergeometric seriessimultaneous approximation\(q\)-hypergeometric series

Mathematics Subject Classification ID

Padé approximation (41A21) Generalized hypergeometric series, ({}_pF_q) (33C20) Simultaneous approximation (41A28) Basic hypergeometric functions (33D99)

Related Items (9)

Hermite-Thue equation: Padé approximations and Siegel's lemma ⋮ \(q\)-blossoming and Hermite-Padé approximants to the \(q\)-exponential function ⋮ Simultaneous Padé approximants to the Euler, exponential and logarithmic functions ⋮ Euler's factorial series and global relations ⋮ Blossoming and Hermite-Padé approximation for hypergeometric series ⋮ Diagonal convergence of the remainder Padé approximants for the Hurwitz zeta function ⋮ Euler's factorial series at algebraic integer points ⋮ A NONVANISHING LEMMA FOR CERTAIN PADÉ APPROXIMATIONS OF THE SECOND KIND ⋮ A p-adic lower bound for a linear form in logarithms

Cites Work

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• Some explicit formulae in simultaneous Padé approximation
• Remainder Padé approximants for the exponential function
• On \(q\)-analogues of divergent and exponential series
• Approximants de Padé simultanés de logarithmes. (Simultaneous Padé approximants of logarithms)
• Padé approximations to the generalized hypergeometric functions. I
• A new proof of the irrationality of \(\zeta (2)\) and \(\zeta (3)\) using Padé approximants
• Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions
• On Siegel–Shidlovskii's theory for q-difference equations

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