What's the Fourier Transform of an Error Function?

Asked Mar 14 '14 at 20:23

Active Mar 15 '14 at 00:16

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What is the Fourier transform of $\displaystyle \operatorname{Erf}\left[a+bx^{2}\right] $?

I need this in order to evaluate

$$ \int_{-\infty}^{\infty}e^{-\beta x^{2}}Erf\left[a+bx^{2}\right]dx $$

using Parseval's theorem:

$$\int_{-\infty}^{\infty} dx \, f(x) g(x) = \frac1{2 \pi} \int_{-\infty}^{\infty} dk \, F(k) G(k)$$

edited Mar 14 '14 at 22:16

asked Mar 14 '14 at 20:23

apg

ok i'll explain further...edit coming.... – apg Mar 14 '14 at 22:13
edit done...this technique may not work though... – apg Mar 14 '14 at 22:17
...the integral would be good, Parseval is only a suggestion – apg Mar 14 '14 at 22:18
1

The fourier transform of $\text{erf}(x)$ can be found in another post: http://math.stackexchange.com/questions/1244744/fourier-transform-of-the-error-function-erf-x/1244745#1244745 – SDiv Jul 28 '15 at 10:00
Thanks! I must have missed it. – apg Jul 28 '15 at 13:09

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