The asymptotic of the weighted Lp-norms of Hermite polynomials is determined for n→∞ 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.
Asymptotical analysis, orthogonal polynomials, information entropy
Publication language:english, pages:22
Mathematical problems and theory of numerical methods