Remainder Pade Approximants for the Exponential Function |
| |
Authors: | Marc Prevost Tanguy Rivoal |
| |
Institution: | (1) Universite du Littoral, Cote d'Opale, Centre Universitaire de la Mi-Voix, Bat H. Poincare, 50 rue F. Buisson, BP 699, 62228 Calais Cedex, France;(2) Institut Fourier, CNRS UMR 5582, Universite Grenoble 1, 100 rue des Maths, BP 74, 38402 Saint-Martin d'Heres Cedex, France |
| |
Abstract: | Following our earlier research, we propose a new method for obtaining the complete Pade table of the exponential function.
It is based on an explicit construction of certain Pade approximants, not for the usual power series for exp at 0 but for
a formal power series related in a simple way to the remainder term of the power series for exp. This surprising and nontrivial
coincidence is proved more generally for type II simultaneous Pade approximants for a family
with distinct complex a's and we recover Hermite's classical formulas. The proof uses certain discrete multiple orthogonal
polynomials recently introduced by Arvesu, Coussement, and van Assche, which generalize the classical Charlier orthogonal
polynomials. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|