Prove that [int_{-infty}^{infty} exp (t x) phi(x) H_{k}(x) d x=t^{k} exp left(frac{1}{2} t^{2}ight)]
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Prove that
\[\int_{-\infty}^{\infty} \exp (t x) \phi(x) H_{k}(x) d x=t^{k} \exp \left(\frac{1}{2} t^{2}ight)\]
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