Fourier Transform--Gaussian
The Fourier Transform of a Gaussian Function 
is given by
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The second integrand is Even, so integration over a symmetrical range gives 0. The value of the first integral is givenby Abramowitz and Stegun (1972, p. 302, equation 7.4.6)
so a Gaussian transforms to a Gaussian.See also Gaussian Function
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.
- Cauchy Sequence
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