Padé approximations to the logarithm I: Derivation via differential equations
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. © 2005 NISC Pty Ltd.