Quick Padé approximations

Extract

Padé approximations consist of one polynomial divided by another (analogous to the polynomial approximations obtained from Maclaurin series). They can serve, at an elementary level, as a corrective to the idea that a power series is the only form of useful approximation. Indeed, they are more powerful than Maclaurin approximations, since, in general, a suitably chosen Padé approximation of a given order gives greater accuracy and is useful over a wide range than the corresponding Maclaurin approximation.