Question: Approximations to complicated functions


I'm working with some rather complicated functions in Maple. They are elements in matrices, and I need to perform mattrix operations on them, as well as integrations. When I try this with my complete functions, Maple locks up. Therefore I am trying to make approximations to some of the functions. The example below shows an example, where the complicated function (green) is denoted theta24. I comvert it to a 5th degree polynomial (red). But the approximation only matches around r=0. I need it to match the original function from r=-1 to r=1. Are there any other approximation method that would work better for me?

Screenshot of Maple desktop

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