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Sum of GaussiansQ: I would like to find a closed form for the sum
Clearly is periodic with unit period (put and ). How can I compute the Fourier series expansion of ? A: Putting and into the formula functions.wolfram.com/09.03.06.0019.01,
that is,
we can express the sum in terms of EllipticTheta as follows:
The Fourier series expansion of (essentially its standard definition) is given at functions.wolfram.com/09.03.06.0001.01,
Here are the first few terms of the Fourier series expansion of .
Note that the Fourier coefficients decrease extremely rapidly.
An excellent approximation is obtained by keeping just the first term in the sum, that is, .


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