Original Articles

Padé Approximations to the Logarithm I: Derivation Via Differential Equations

Published in: Quaestiones Mathematicae
Volume 28 , issue 3 , 2005 , pages: 375–390

DOI: 10.2989/16073600509486135

Author(s): J.A.C. Weideman

Keywords: PADE APPROXIMATION , FROBENIUS' METHOD , FINITE DIFFERENCES , LAPLACE TRANSFORMS

Abstract

Explicit formulas for the polynomials that define Hermite-Padé approximations to the logarithm are derived. The main elements of the derivation are Frobenius' method for solving linear differential equations, and automatic summation algorithms. Applications to finite difference formulas and Laplace transforms are indicated.

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