The function pade computes a Pade approximation of degree  for the function f with respect to the variable x.

Specifically, f is expanded in a Taylor (or Laurent) series about the point  (if a is not specified then the expansion is about the point ), to order , and then the Pade rational approximation is computed.

The  Pade approximation is defined to be the rational function  with  and  such that the Taylor (or Laurent) series expansion of  has maximal initial agreement with the series expansion of f. In normal cases, the series expansion agrees through the term of degree .

If  or if the third argument is simply an integer m then the Taylor (or Laurent) polynomial of degree m is computed.

Various levels of user information will be displayed during the computation if infolevel[pade] is assigned values between 1 and 3.

The command with(numapprox,pade) allows the use of the abbreviated form of this command.