Legendre-Pade Approximation

Computes the Legendre Pade approximation to an analytic function.

Computes a rational approximation to an analytic function using Legendre Polynomials. Sample a function f(x) at the Legendre-Gauss-Lobatto nodes (see requirements) and this script computes the Legendre expansion coefficients of the functions a(x) and b(x) such that a/b~=f.

Note f(x) must have a locally convergent Taylor series.