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.
