The Wikipedia article on Padé approximant makes it sound like "Padé series" is capable of approximating a function better than Taylor series can.
Can Padé series be treated as a drop-in replacement for Taylor series approximation in non-linear least squares (NLLS)? Would it even make sense to use Padé approximant instead of Taylor series in NLLS (and would it bring any benefits like faster convergence or being less prone to end up in local minima or maxima)? Are there any real-world examples?