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Keldysh Institute preprints, 2012, 070, 22 pp. (Mi ipmp88)  

Asymptotics of $L_p$-norms of Hermite polynomials

A. I. Aptekarev, D. N. Tulyakov


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

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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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