ABSTRACT
A rational function is a function which can be represented in the form p(x)/q(x) where p(x) and q(x) are polynomials. When p(x) has degree m and q(x) has degree n, we shall say that the ratio has degree (m, n).
As was discussed earlier in the last chapter, both power series and asymptotic series share the common property that their partial sums are rational functions. So a natural extension of our investigations is a theory by which general functions may be locally approximated by rational functions. Taylor’s theorem and Taylor polynomials provide the theoretical basis for the use of polynomial approximations to analytic functions. The corresponding theory for rational functions leads to the class of Pade´ approximants.
