Padé-type approximants for generalized Euler transforms

Paul Sablonnière (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We prove that sequences generated by the generalized Euler's transform can be considered as Padé-type approximants obtained by Hermite interpolation of the generating function (1+xu)^{-1} at the endpoints of the interval [0,1]. A first natural extension is then proposed by considering Hermite interpolation at multiple points of larger intervals.

Mots clés: Padé-type approximants; Generalized Euler's transform

Domaines: Analyse numérique [math.NA]

Paul Sablonnière. Padé-type approximants for generalized Euler transforms. Numerical Algorithms, 2014, 66 (2), pp.339-347. ⟨10.1007/s11075-013-9737-4⟩. ⟨hal-00786065⟩