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