PadeApproximant
Computes the [m/n] Padé approximant of a function about a point: the rational
function P(x)/Q(x) with deg P <= m, deg Q <= n and Q(x0) = 1, whose
power series agrees with the function through order m + n.
$ wo 'PadeApproximant[Exp[x], {x, 0, {2, 2}}]'
(1 + x/2 + x^2/12)/(1 - x/2 + x^2/12)
$ wo 'PadeApproximant[Cos[x], {x, 0, {2, 2}}]'
(1 - (5*x^2)/12)/(1 + x^2/12)
$ wo 'PadeApproximant[Log[1 + x], {x, 0, {2, 2}}]'
(x + x^2/2)/(1 + x + x^2/6)
$ wo 'PadeApproximant[ArcTan[x], {x, 0, {3, 2}}]'
(x + (4*x^3)/15)/(1 + (3*x^2)/5)
With denominator degree 0 the result is just the Taylor polynomial:
$ wo 'PadeApproximant[Exp[x], {x, 0, {2, 0}}]'
1 + x + x^2/2