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Math Help - convergence test for integral

  1. #1
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    convergence test for integral

    hey there.. i'm kinda lost here..
    i need to do convergence test for the equation below...
    y(x)=\frac{1}{\sqrt{2\pi}}\frac{1}{a}\sqrt{\frac{\  pi}{a}}\int_{-\infty}^{\infty} e^{-a|x|}f(x-t)dt

    however.. i've got 2 value of f(x).. e^x^2 and x^5

    how am i going to test them?
    should i include my f(x) inside the equation above?
    like this...
    y(x)=\int_{-\infty}^{\infty} e^{-a|x|}f(x-t)^{5}dt

    and..

    y(x)=\int_{-\infty}^{\infty} e^{-a|x|}f(e^{(x-t)^{2}})dt

    please guide me..

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  2. #2
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    If f(x) = x^5, then the substitution gives

    y(x)=(constants)\int_{-\infty}^{\infty} e^{-a|x|}(x-t)^{5}dt

    Similarly,

    If f(x) = e^{x^2}, then the substitution gives

    y(x)=(constants)\int_{-\infty}^{\infty} e^{-a|x|}e^{(x-t)^{2}}dt
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  3. #3
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    how am i going to test the equations?
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