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Math Help - Function defined by a series

  1. #1
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    Function defined by a series

    I've this problem, maybe I should use M-weierstrass test, but I really don't know. I appreciate your help.
    I must find the domain of the function, the biggest set where the function is continuous and the biggest set where the function is differentiable.

    f(x) = \displaystyle \sum_{n=0}^\infty \frac{e^{-nx}}{n^2+1}

    Thanks
    everk
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  2. #2
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    The series converges (pointwise) only for nonnegative x, apply Weierstrass to show continuity here, and then find an interval where the series of termwise derivatives converge uniformly (for this last one I only found that the series converges uniformly in (b,\infty ) where b=\sup_{n\geq 1} \{n^{1/n}\}, but I'm not sure it's the biggest)
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