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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.

    Thanks
     
  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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