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I would like to calculate the Fourier transform of the function: $\frac{e^{-k(x-k)^2}}{x}$ but the integral $$\int_{-\infty}^{+\infty} \frac{e^{-k(x-k)^{2}}}{x} \ e^{i\omega x}\,dx$$ it is very difficult for me. Any suggestions?

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Have you tried using convolutions? en.wikipedia.org/wiki/Convolution_theorem –  George Lowther May 23 '12 at 23:05

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