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I Complex integral

  1. Jun 8, 2017 #1
    Hello! I found a proof in my physics books and at a step it says that: ##\int_m^\infty\sqrt{x^2-m^2}e^{-ixt}dx \sim_{t \to \infty} e^{-imt}##. Any advice on how to prove this?
  2. jcsd
  3. Jun 8, 2017 #2

    Buzz Bloom

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    Gold Member

    Hi @Silviu:

    Here is a thought that might help.

    Substitute x= y+m. This will produce e-imt F(t)
    F(t) = Inverse Fourier Transform of f(x)
    f(x) = √(y (y+2m)).
    Therefore, this reduces the problem to prove lim[t→∞] F(t) = 1.

    Good luck.

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