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Math Help - Uniform convergence of a sequence of functions

  1. #1
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    Uniform convergence of a sequence of functions

    Hi, I was hoping someone might be able to help me out.

    Can the following sequence of function be differentiated?



    As far as I understood, I have to check continuity and uniform convergence. I think it fails to satisfy the latter. How can I explain it?
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  2. #2
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    Quote Originally Posted by BMWM5 View Post
    Hi, I was hoping someone might be able to help me out.

    Can the following sequence of function be differentiated?



    As far as I understood, I have to check continuity and uniform convergence. I think it fails to satisfy the latter. How can I explain it?
    Actually, you need uniform convergence of the term-by-term derivative \sum_{n=1}^\infty\frac{1}{x^2+n^2}. This one is easy to prove (cf. normal convergence).
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  3. #3
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    I think I got it, thanks.

    BTW, isn't the derivative ? (It doesn't make a difference anyway )
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  4. #4
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    Quote Originally Posted by BMWM5 View Post
    I think I got it, thanks.

    BTW, isn't the derivative ? (It doesn't make a difference anyway )
    Yes, sorry. And indeed, the proof procedes the same way.
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