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Math Help - periodic

  1. #1
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    periodic

    I have this:
    f is continuous on a closed interval [a,b] on a real line.
    I defined g(x)=f(a+(b-a)x/pi) for x in closed interval [0,pi] such that f cont. on [a,b] is symmetric to function g over a the new interval [0,pi].

    My question is how do I show that g is periodic?
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  2. #2
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    Quote Originally Posted by chihahchomahchu View Post
    I have this:
    f is continuous on a closed interval [a,b] on a real line.
    I defined g(x)=f(a+(b-a)x/pi) for x in closed interval [0,pi] such that f cont. on [a,b] is symmetric to function g over a the new interval [0,pi].
    My question is how do I show that g is periodic?
    Why do you think that it is periodic?

    Have you actually taken examples?
    Say: a=1,~b=4,~\&~f(x)=\frac{1}{x}
    Graph that. What do you see?
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  3. #3
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    Quote Originally Posted by Plato View Post
    Why do you think that it is periodic?

    Have you actually taken examples?
    Say: a=1,~b=4,~\&~f(x)=\frac{1}{x}
    Graph that. What do you see?
    Sorry for lack of information. I am derive from the Fejer-cesaro approximation theorem to prove Weierstrass approximation theorem. Fejer-cesaro theorem is periodic 2pi. In order for me to use Fejer-cesaro theorem, I need to do a change of variable of function f cont. on [a,b] to new function and new interval, so I can define the Fourier nth partial sum.

    How do I make this new function periodic?
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  4. #4
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    in other word, let f(-x)=f(x), x in [0,pi], How do I take the unique periodic extension of this function?
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