Complexity-like properties and parameter asymptotics of Lq -norms of Laguerre and Gegenbauer polynomials

The main monotonic statistical complexity-like measures of the Rakhmanov's probability density associated to hypergeometric orthogonal polynomials (HOPs) in a real continuous variable, each them quantifying two configurational facets spreading, are examined this work beyond Cram\'er-Rao one. Fisher-Shannon and LMC (L\'opez-Ruiz-Mancini-Calvet) complexity measures, which have entropic components, analytically expressed terms degree orthogonality weight's parameter(s) polynomials. parameter asymptotics these two-fold spreading shown for parameter-dependent families HOPs Laguerre Gegenbauer types. This is done by using R\'enyi Shannon entropies, closely connected $\mathfrak{L}_{q}$-norms polynomials, when tends towards infinity. algebraic norms control radial angular charge momentum distributions numerous relevant multidimensional physical systems with spherically-symmetric quantum-mechanical potential high-energy (Rydberg) high-dimensional (quasi-classical) states, respectively. because corresponding states' wavefunctions means both position spaces.