Remainder Padé approximants for the exponential function (Q854990)

The authors study a new method for obtaining the complete Padé table the exponential function. The aim of this paper is to show that this table of Padé approximants for the function \(\exp(z)\) at \(z=0\) essentially coincide with the approximation obtained by the method described in [\textit{S. Fischler} and \textit{T. Rivoal}, Approximants de Padé et séries hypergéométriques équilibrées, J. Math. Pures. Appl. 82, 1369--1394 (2003; Zbl 1064.11053)]. The authors call it the remainder Padé approximants for \(\exp(z)\). The results deal more generally with simultaneous type II Padé approximations of a family of exponential functions. The proof uses certain discrete multiple orthogonal polynomials recently introduced by Arvesú, Coussement, and Van Assche which generalize the classical Charlier orthogonal polynomials.