Let-a-gt-0-g-x-n-Z-exp-x-n-2-a-Find-the-Fourier-coefficients-of-g-and-deduce-that-for-x-R-n-Z-exp-pin-2-x-2-x-n-Z-exp-pin-2-x-2-

Question Number 120528 by snipers237 last updated on 01/Nov/20

L e t a > 0, g (x) = \sum_{n \in Z} e x p (- \frac{{(x - n)}^{2}}{a})

F i n d t h e F o u r i e r c o e f f i c i e n t s o f g

a n d d e d u c e t h a t f o r x \in R^{*}

\sum_{n \in Z} e x p (- \frac{π n^{2}}{x^{2}}) = x . \sum_{n \in Z} e x p (- π n^{2} x^{2})