Taylor series only approximate an (infinitely differentiable) function well locally, i.e. in some neighborhood of the approximation point. There are other metho

Taylor series only approximate an (infinitely differentiable) function well locally, i.e. in some neighborhood of the approximation point. There are other methods applicable to less smooth functions and which approximate well uniformly (bounding the maximum absolute error) or by some other metric (e.g. L2 distance — integrated squared error).