Padé approximant

PADE gives the Padé approximant of order [N/M] to the function F about the point Xo.

The Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. For these reasons Padé approximants are used extensively in computer calculations.

The user-supplied function must return the value of the derivatives up to (N + M)-th, where N and M are the degree of the numerator and denominator of the rational approximant form