Blossoming and Hermite-Padé approximation for hypergeometric series

Rachid Haddou, Marie Laurence Mazure

Research output: Contribution to journalJournal articlepeer-review

Abstract

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.

Original languageEnglish
JournalNumerical Algorithms
DOIs
StateAccepted/In press - 2021

Keywords

  • Blossoms
  • Hermite identity
  • Hermite-Padé approximation
  • Hypergeometric series
  • q-Blossoms
  • Rational approximation

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