gives the economized rational approximation to expr that is good over the interval x0 to x1, with numerator order m and denominator order n.

Details and Options

  • To use EconomizedRationalApproximation, you first need to load the Function Approximations Package using Needs["FunctionApproximations`"].
  • EconomizedRationalApproximation finds the Padé approximant about the midpoint of the interval x0 to x1, and then perturbs the approximant with Chebyshev polynomials to reduce the leading coefficient in the error.
  • The Wolfram Language can find the economized rational approximant over the interval x0 to x1 only when it can evaluate power series at the midpoint of the interval.
  • EconomizedRationalApproximation produces a ratio of ordinary polynomial expressions, not a special SeriesData object.