LAUSR

. The three canonical families of the hypergeometric orthogonal polynomials (Hermite, Laguerre and Jacobi) control the physical wavefunctions of the bound stationary states of a great deal of quantum systems. The algebraic L q -norms of these polynomials describe many physical, chemical and information-theoretical properties of these systems, such as e.g. the kinetic and Weizs¨acker energies, the position and momentum expectation values, the R´enyi and Shannon entropies and the Cram´er-Rao, the Fisher-Shannon and LMC measures of complexity. In this work we examine, partially review and solve the q -asymptotics and the parameter asymptotics (i.e., when the weight function’s parameter tends towards infinity) of the unweighted and weighted L q -norms for these orthogonal polynomials. This study has been motivated by the application of these algebraic norms to the energetic, entropic and complexity-like properties of the highly-excited