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Remainder Padé approximants for the exponential function. (English) Zbl 1102.41016
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 [S. Fischler and 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.

##### MSC:
 41A21 Padé approximation 41A28 Simultaneous approximation