Padé approximants for the q-elementary functions

DOI10.1007/BF02075469zbMath0685.41015WikidataQ56453653 ScholiaQ56453653MaRDI QIDQ1826059

Peter B. Borwein

Publication date: 1988

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

zbMATH Keywords

theta functionPadé approximantslogarithmic functionHermite-Padé approximantsq-logarithmq-analogues

Mathematics Subject Classification ID

Padé approximation (41A21)

Related Items (18)

Convergence of Padé approximants for a \(q\)-hypergeometric series (Wynn's power series III) ⋮ On the irrationality of a certain multivariate $q$ series ⋮ On the irrationality of \(\sum (1/(q^ n+r))\) ⋮ \(q\)-blossoming and Hermite-Padé approximants to the \(q\)-exponential function ⋮ Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ Approximants de Padé et $U$-dérivation ⋮ Explicit construction of multivariate Padé approximants for a \(q\)-logarithm function ⋮ Convergence of Padé approximants for a \(q\)-hypergeometric series (Wynn's power series I) ⋮ Blossoming and Hermite-Padé approximation for hypergeometric series ⋮ Explicit construction of multivariate Padé approximants ⋮ Arithmetic properties of solutions of certain Poincaré-type functional equations ⋮ Explicit construction of general multivariate Padé approximants to an Appell function ⋮ Some applications of theq-Rice formula ⋮ Multivariate Padé approximants to a meromorphic function ⋮ General order multivariate Padé approximants for pseudo-multivariate functions ⋮ Multivariate Padé approximants associated with functional relations ⋮ On the irrationality of certain series ⋮ \(U\)-derivation

Cites Work

• Unnamed Item
• Unnamed Item
• Rationale Approximation des \(q\)-Analogons der Exponentialfunktion und Irrationalitätsaussagen für diese Funktion. (Rational approximation of the \(q\)-analogue of the exponential function and irrationality statements for this function)
• The asymptotic accuracy of rational best approximations to \(e^ z\) on a disk
• On the zeros and poles of Padè approximants to \(e^z\). III
• Shanks' convergence acceleration transform, Padé approximants and partitions
• Recurrence relations, continued fractions, and orthogonal polynomials
• A GENERAL SYSTEM OF ORTHOGONAL POLYNOMIALS

This page was built for publication: Padé approximants for the q-elementary functions