Blossoming and Hermite-Padé Approximation for Hypergeometric Series
| Autor: | Marie-Laurence Mazure, Rachid Ait-Haddou |
|---|---|
| Přispěvatelé: | King Fahd University of Petroleum and Minerals (KFUPM), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Hermite polynomials
Series (mathematics) q-Blossoms Applied Mathematics Mathematics::Classical Analysis and ODEs Hermite-Padé approximation 010103 numerical & computational mathematics 16. Peace & justice 01 natural sciences Hermite identity Blossoms Hypergeometric series Exponential function 010101 applied mathematics Algebra Identity (mathematics) Rational approximation MSC: 65D17 65D20 41A20 41A21 41A28 Theory of computation Padé approximant 0101 mathematics Hypergeometric function [MATH]Mathematics [math] Binomial series Mathematics |
| Zdroj: | Numerical Algorithms Numerical Algorithms, Springer Verlag, 2021, 88, pp.1183-1214. ⟨10.1007/s11075-021-01071-3⟩ Numerical Algorithms, 2021, 88, pp.1183-1214. ⟨10.1007/s11075-021-01071-3⟩ |
| ISSN: | 1017-1398 1572-9265 |
| DOI: | 10.1007/s11075-021-01071-3⟩ |
| Popis: | International audience; Based on the blossoming theory, in this work we develop a new method for deriving Hermite-Padé approximants of certain hypergeometric series. Its general principle consists in building identities generalising the Hermite identity for exponentials, and in then applying their blossomed versions to appropriate tuples to simultaneously produce explicit expressions of the approximants and explicit integral representations of the corresponding remainders. For binomial series we use classical blossoms while for q-hypergeometric series we have to use q-blossoms. |
| Databáze: | OpenAIRE |
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