{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T04:12:35Z","timestamp":1773720755168,"version":"3.50.1"},"reference-count":92,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,3]],"date-time":"2021-08-03T00:00:00Z","timestamp":1627948800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2019s probability density\u2014so, far beyond the standard deviation and its generalizations, the ordinary moments. The Fisher information, the R\u00e9nyi 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 (R\u00e9nyi, 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.<\/jats:p>","DOI":"10.3390\/sym13081416","type":"journal-article","created":{"date-parts":[[2021,8,3]],"date-time":"2021-08-03T23:37:21Z","timestamp":1628033841000},"page":"1416","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Entropy-Like Properties and Lq-Norms of Hypergeometric Orthogonal Polynomials: Degree Asymptotics"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4397-9426","authenticated-orcid":false,"given":"Jes\u00fas S.","family":"Dehesa","sequence":"first","affiliation":[{"name":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071 Granada, Spain"},{"name":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,3]]},"reference":[{"key":"ref_1","unstructured":"Szeg\u00f6, G. 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