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As it's been awhile I thought I'd submit Max Alekseyev's comment as an answer so that this question is seen as answered.

The simplify command f(a,x).simplify() does indeed work to evaluate sums inside of symbolic functions. But it seems one has to type the .simplify() method manually each time as it can't effectively be added to the function.

On the other hand, Python's lambda function f = lambda m,x: 4/pi*sum(term(k,x) for k in range(m+1)) evaluates without flaw and seems to retain the advantages of symbolic functions, like differentiability.

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As it's been awhile I thought I'd submit Max Alekseyev's comment as an answer so that this question is seen as answered.complete.

The simplify command f(a,x).simplify() does indeed work to evaluate sums inside of symbolic functions. But it seems one has to type the .simplify() method manually each time as it can't effectively be added to the function.

On the other hand, Python's lambda function f = lambda m,x: 4/pi*sum(term(k,x) for k in range(m+1)) evaluates without flaw and seems to retain the advantages of symbolic functions, like differentiability.