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It must be proven that the solution of the integral equation $$f(x)=\int_{-\infty}^{+\infty} e^{-(x-t)^2} g(t)dt$$ is $$g(x)=\frac{1}{\sqrt{}\pi}\sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{2^nn!} H_n(x)$$

where the $H_n(x)$ are the Hermite polynomials.

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    What is $f$? $ $2011-12-18
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    It looks like a Fredholm equation of the first kind... the sort that's usually solved with a Fourier transform.2011-12-19

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