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Preprints of the Keldysh Institute of Applied Mathematics, 2012, 070, 22 pp. (Mi ipmp88)  
Asymptotics of $L_p$-norms of Hermite polynomials

A. I. Aptekarev, D. N. Tulyakov
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Abstract: The asymptotic of the weighted $L_p$-norms of Hermite polynomials is determined for $n \to \infty$ and $p>0$. The result is motivated by calculations the Rényi entropy of the quantum-mechanical probability density of the highly-excited (Rydberg) states of the isotropic oscillator.
Keywords: Asymptotical analysis; orthogonal polynomials; information entropy.
Document Type: Preprint
Language: English
Citation: A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of $L_p$-norms of Hermite polynomials”, Keldysh Institute preprints, 2012, 070, 22 pp.
Citation in format AMSBIB
\Bibitem{AptTul12}
\by A.~I.~Aptekarev, D.~N.~Tulyakov
\paper Asymptotics of $L_p$-norms of Hermite polynomials
\jour Keldysh Institute preprints
\yr 2012
\papernumber 070
\totalpages 22
\mathnet{http://mi.mathnet.ru/ipmp88}
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    		Препринты Института прикладной математики им. М. В. Келдыша РАН
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