Comment by davrosthedalek

Taylor series have a quite different convergence behavior than a general polynomial approximation. Or polynomial fit for that matter. Many papers were written which confuse this.

For example, 1/(x+2) has a pole at x=-2. The Taylor series around 0 will thus not converge for |x|>2. A polynomial approximation for, say, a range 0<x<L, will for all L.