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EconomizedRationalApproximation[expr, {x, {x0, x1}, m, n}]
gives the economized rational approximation to expr that is good over the interval x0 to x1, with numerator order m and denominator order n.
  • 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.
  • Mathematica 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.