You can use both at the same time for extremely nice results. Compute some truncated Chebyshev polynomial approximation (i.e. the first few terms) and then use Pade approximation [1]. The cool part about this is that you can prescribe your maximum allowed error (between exact solution and approximation) ahead of time, and compute the order of the Pade approximation that under all circumstances guarantees that your error will be bounded!
is there a way to have Pade approximation but with continued fractions, so you just truncate the series as necessary? I tried looking into this a few months ago, but my head just started to hurt.
