The Pade approximation is a form of rational approximation which is analogous to the Taylorapproximation because it is based on the derivatives of  f(x) at x=0.  The Pad� approximation is very accurate near the center of expansion.  However, the error increases as one moves away from the center of expansion.  More accurate rational approximations are obtained if "interpolation nodes" are used, and we permit the error to be spread out more evenly over the entire interval.  The process is similar to Lagrange and Chebyshev interpolation.