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Math Help - Help in Finding the Fourier Sine Transform

  1. #1
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    Question Help in Finding the Fourier Sine Transform

    I need your help in finding the Fourier Sine Transform of (x^(n-1))
    Last edited by sunveer; August 26th 2011 at 08:14 AM. Reason: Correcting the expression
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  2. #2
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    Re: Help in Finding the Fourier Sine Transform

    Two questions:

    1. What is your definition of the Fourier Sine Transform? (There are more than one.)
    2. What integral are you then supposed to compute?
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  3. #3
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    Re: Help in Finding the Fourier Sine Transform

    My definition.

    ( \sqrt 2/ \pi) \int (from 0 to infinity) x^{n-1}sinsx.dx
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    Re: Help in Finding the Fourier Sine Transform

    Just to clarify:

    \mathcal{F}_{s}[x^{n-1}]:=\sqrt{\frac{2}{\pi}}\int_{0}^{\infty}x^{n-1}\sin(sx)\,dx.

    Correct? Or is it


    \mathcal{F}_{s}[x^{n-1}]:=\frac{\sqrt{2}}{\pi}\int_{0}^{\infty}x^{n-1}\sin(sx)\,dx?

    Assuming one of these forms is correct (I'm guessing the first), what thoughts have you had so far?
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  5. #5
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    Re: Help in Finding the Fourier Sine Transform

    Quote Originally Posted by sunveer View Post
    My definition.

    ( \sqrt 2/ \pi) \int (from 0 to infinity) x^{n-1}sinsx.dx
    What are the restrictions on n ?

    CB
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  6. #6
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    Re: Help in Finding the Fourier Sine Transform

    The first form is correct. You are right.

    Also, there are no restrictions on 'n'
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  7. #7
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    Re: Help in Finding the Fourier Sine Transform

    See here. I don't know if the link I posted will get you the "Allow More Time" option, but you'll need to click that, if it doesn't give you the answer right away. You'll note the restrictions on n in the final result, as well as the restriction on s. Mathematica doesn't give an answer if those restrictions aren't met. I suspect the integral may not actually exist in that situation.
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