Blossoming and Hermite-Padé Approximation for Hypergeometric Series

Rachid Ait-Haddou (1) , Marie-Laurence Mazure (2)

1 KFUPM - King Fahd University of Petroleum and Minerals
2 CVGI - Calcul des Variations, Géométrie, Image

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.

Mots clés: Rational approximation; Hermite-Padé approximation; Hypergeometric series; Hermite identity; Blossoms; q-Blossoms

Domaines: Mathématiques [math]

Rachid Ait-Haddou, Marie-Laurence Mazure. Blossoming and Hermite-Padé Approximation for Hypergeometric Series. Numerical Algorithms, 2021, 88, pp.1183-1214. ⟨10.1007/s11075-021-01071-3⟩. ⟨hal-02996917⟩