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I am wondering if someone knows good references. I am looking for expansions of Hermite functions, which gives connections between rates of decay and smoothness of coefficients.

Thank you for your suggestions.

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I've found Special Functions: An Intro. to the Classical Functions of Mathematical Physics by Nico Temme very helpful.

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I don't think there's anything in that book about Hermite expansions. – TrialAndError Feb 2 '15 at 18:59

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