Entropy-Like Properties and Lq-Norms of Hypergeometric Orthogonal Polynomials: Degree Asymptotics

In this work, the spread of hypergeometric orthogonal polynomials (HOPs) along their orthogonality interval is examined by means main entropy-like measures associated Rakhmanov’s probability density—so, far beyond standard deviation and its generalizations, ordinary moments. The Fisher information, Rényi Shannon entropies, corresponding spreading lengths are analytically expressed in terms degree parameter(s) weight function. These entropic quantities closely related to gradient functional (Fisher) Lq-norms (Rényi, Shannon) polynomials. addition, asymptotics for these functionals three canonical families HPOs (i.e., Hermite, Laguerre, Jacobi polynomials) given briefly discussed. Finally, a number open issues identified whose solutions both physico-mathematically computationally relevant.