Entropy-Like Properties and L-q-Norms of Hypergeometric Orthogonal Polynomials: Degree Asymptotics Sánchez-Dehesa Moreno-Cid, Jesús Special functions Classical orthogonal polynomials Entropy-like measures Asymptotics This work was partially supported by the Agencia Estatal de Investigacion (Spain) and the European Regional Development Fund (FEDER) under the grant PID2020-113390GB-I00. In this work, the spread of hypergeometric orthogonal polynomials (HOPs) along their orthogonality interval is examined by means of the main entropy-like measures of their associated Rakhmanov’s probability density—so, far beyond the standard deviation and its generalizations, the ordinary moments. The Fisher information, the Rényi and Shannon entropies, and their corresponding spreading lengths are analytically expressed in terms of the degree and the parameter(s) of the orthogonality weight function. These entropic quantities are closely related to the gradient functional (Fisher) and the Lq-norms (Rényi, Shannon) of the polynomials. In addition, the degree asymptotics for these entropy-like functionals of the three canonical families of HPOs (i.e., Hermite, Laguerre, and Jacobi polynomials) are given and briefly discussed. Finally, a number of open related issues are identified whose solutions are both physico-mathematically and computationally relevant. 2021-10-13T08:52:21Z 2021-10-13T08:52:21Z 2021-08-03 info:eu-repo/semantics/article Dehesa, J.S. Entropy-Like Properties and Lq-Norms of Hypergeometric Orthogonal Polynomials: Degree Asymptotics. Symmetry 2021, 13, 1416. [https://doi.org/10.3390/sym13081416] http://hdl.handle.net/10481/70819 10.3390/sym13081416 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI