Fourier transform of a gaussian

[sleventh]

fourier transform of the gaussian (1/\sqrt{2 pi \sigma}) e ^ (^{x^2/2\sigma^2})



now the Fourier of a gaussian is said to equal another gaussian as shown by equation (4) here:
http://mathworld.wolfram.com/FourierTransform.html

but when i also did it using equation (1) here:
http://mathworld.wolfram.com/FourierTransform.html

i find a completely different answer.

im wondering how i am doing the calculations wrong using the normal definition of Fourier transforms.

fourier transforms are very new to me so any help is much appreciated thank you.

 

[lanedance]

you'll have more chance if you show you working, its pretty hard to guess what you're doing wrong

 

[sleventh]

setting a=1/2 \sigma ^2 and k=1/2\sqrt{2 pi sigma} i use the concept the Fourier of a gaussian equals another gaussian and am given
\sqrt{2 sigma ^2 pi} e^((-2pi^2 \sigma^2 / \sqrt{2 pi sigma}