Convergence of Padé approximants for a \(q\)-hypergeometric series (Wynn's power series I)

DOI10.1007/BF01818481zbMath0746.41021OpenAlexW4236150986MaRDI QIDQ1180549

Doron S. Lubinsky, Kathy A. Driver

Publication date: 27 June 1992

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/137421

zbMATH Keywords

Padé approximants

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Padé approximation (41A21) Moment problems and interpolation problems in the complex plane (30E05)

Related Items

Convergence of Padé approximants for a \(q\)-hypergeometric series (Wynn's power series III) ⋮ Reflections on the Baker–Gammel–Wills (Padé) Conjecture ⋮ Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities ⋮ Irregular distribution of \(\{n\beta{}\} \), \(n=1,2,3,\)\dots , quadrature of singular integrands, and curious basic hypergeometric series ⋮ Convergence of simultaneous Hermite-Padé approximants to the \(n\)-tuple of \(q\)-hypergeometric series \(\{_ 1\Phi_ 1 (_{c,\gamma_ j}^{(1,1)};z)\}_{j=1}^ n\) ⋮ Multivariate Padé approximants associated with functional relations ⋮ The size of \((q;q)_n\) for \(q\) on the unit circle ⋮ On the radius of convergence of \(q\)-series ⋮ Convergence of simultaneous Hermite-Padé approximants to the \(n\)-tuple of \(q\)-hypergeometric series \(\{_ 2\Phi_ 0((A,\alpha_ j), (1,1);z)\}_{j=1}^ n\)

Cites Work

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• Convergence of Padé approximants of partial theta functions and the Rogers-Szegö polynomials
• Diagonal Padé approximants and capacity
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• ON THE CONVERGENCE OF PADÉ APPROXIMANTS IN CLASSES OF HOLOMORPHlC FUNCTIONS
• A GENERAL SYSTEM OF ORTHOGONAL POLYNOMIALS