Remainder Padé approximants for hypergeometric series
Résumé
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).
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