The three canonical families of the hypergeometric orthogonal polynomials in a
continuous real variable (Hermite, Laguerre, and Jacobi) control the physical
wavefunctions of the bound stationary states of a great number of quantum systems
[Correction added after first online publication on 21 December, 2022. The sentence
has been modified.]. The algebraic Lq-norms of these polynomials describe many
chemical, physical, and information theoretical properties of these systems, such as,
for example, the kinetic and Weizsäcker energies, the position and momentum
expectation values, the Rényi and Shannon entropies and the Cramér-Rao, the
Fisher-Shannon and LMC measures of complexity. In this work, we examine 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
Lq-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 Rydberg and high-dimensional pseudo-classical states
of harmonic (oscillator-like) and Coulomb (hydrogenic) systems, and other quantum
systems subject to central potentials of anharmonic type (such as, e.g., some molecu-
lar systems) [Correction added after first online publication on 21 December, 2022.
Oscillatorlike has been changed to oscillator-like.].The work of J.S. Dehesa has been partially supported by the grant I+D+i of Junta de Andalucia with ref. P20-00082, and the grant PID2020-113390GB-I00 of the Agencia Estatal de Investigación (Spain) and the European Regional Development Fund (FEDER). The work of N. Sobrino has been partially supported by the grant IT1249-19 of Basque Government and UPV/EHU
