The asymptotic of the weighted L_{p}-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.

Keywords:

Asymptotical analysis, orthogonal polynomials, information entropy

Publication language:english,
pages:22

Research direction:

Mathematical problems and theory of numerical methods