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Solve this fourier integral

  1. Dec 3, 2003 #1
    Hi to everybody

    I have to solve this fourier integral:

    1) f(q)=\int_{-infty}^{+infty}a*b*x^(b-1)*exp(-a*x^b)*exp(i*q*x)*dx

    and if S_n=x_1+...+x_n, with S_n the sum of n random variables IID, then I can write:

    f_n(q)=[f(q)]^n,(convolution theorem), then the anti-trasform of f_n(q) give the pdf of the variable S_n.

    2) F(S_n)=(1/2*pi)*\int_{-infty}^{+infty}f_n(q)*exp(-i*q*x)*dq.

    I must to solve the equations 1) and 2) in order to solve my problem, the equation 2) is the final solution of the problem.

  2. jcsd
  3. Dec 3, 2003 #2
    Re: problem

    [tex]f(q)=ab\int_{-\infty}^{\infty}x^{b-1}\exp(-a\,x^b) \exp(i \,q\,x)dx[/tex]

    I don't think that this integral has an analytical solution...
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