One may think of the coefficients *c*_{k} as representing a power series expansion of any general function.
In the rational function, one has to set a scale,
usually by defining *b*_{0} = 0. This leaves *m* + *n* + 1 unknowns, the coefficients *a*_{i} and *b*_{i},
for which it is unproblematic to solve: the expression is multiplied with the denominator of the rational function, giving on both sides of the equation polynomials containing the unknown coefficients;
one equates all terms with the same power of *x*
to obtain the solution.

Padé approximations are useful for representing unknown functions with possible poles, i.e. with denominators tending towards zero. For a discussion and algorithm, see [Press95], also [Wong92].

Rudolf K. Bock, 7 April 1998