Remainder Padé approximants for hypergeometric series

Marc Prévost (1) , Tanguy Rivoal (2)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
2 IF - Institut Fourier

Remainder Padé Approximation (RPA) consists in adding to the n-th partial sum of a series a suitable Padé approximant of the asymptotic expansion in the variable 1/n of the remainder term. In a previous paper, we proved the non-trivial property that the RPA of the exponential function is identical to the Padé approximant to the exponential function. In this paper, we extend this property to the hypergeometric series 1F1(1; a; z) and 2F0(b, 1; z).

Mots clés: Remainder Pad ́e approximants; hypergeometric function; multiple Charlier polynomials

Domaines: Théorie des nombres [math.NT]; Analyse numérique [math.NA]

Marc Prévost, Tanguy Rivoal. Remainder Padé approximants for hypergeometric series. Integral Transforms and Special Functions, 2019, 30 (10), pp.833-843. ⟨10.1080/10652469.2019.1624542⟩. ⟨hal-02017857⟩