compute a Pade approximation
pade(f, x=a, [m, n])
pade(f, x, [m, n])
expression representing the function to be approximated
the variable appearing in f
the point about which to expand in a series
desired degree of numerator and denominator, respectively
The function pade computes a Pade approximation of degree m,n for the function f with respect to the variable x.
Specifically, f is expanded in a Taylor (or Laurent) series about the point x=a (if a is not specified then the expansion is about the point x=0), to order m+n+1, and then the Pade rational approximation is computed.
The m,n Pade approximation is defined to be the rational function p⁡xq⁡x with deg⁡p⁡x≤m and deg⁡q⁡x≤n such that the Taylor (or Laurent) series expansion of p⁡xq⁡x has maximal initial agreement with the series expansion of f. In normal cases, the series expansion agrees through the term of degree m+n.
If n=0 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.
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