The determination of the physical entropies (Rényi, Shannon, Tsallis) of high-dimensional quantum systems subject to a central potential requires the knowledge of the asymptotics of some power and logarithmic integral functionals of the hypergeometric orthogonal polynomials which control the wavefunctions of the stationary states. For the D-dimensional hydrogenic and oscillator-like systems, the wavefunctions of the corresponding bound states are controlled by the Laguerre () and Gegenbauer () polynomials in both position and momentum spaces, where the parameter α linearly depends on D. In this work we study the asymptotic behavior as of the associated entropy-like integral functionals of these two families of hypergeometric polynomials.

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Keywords asymptotic analysis of integrals, entropic functionals of Laguerre and Gegenbauer polynomials, information theory of orthogonal polynomials
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Journal Journal of Physics A: Mathematical and Theoretical
Temme, N.M, Toranzo, I.V, & Dehesa, J.S. (2017). Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters. Journal of Physics A: Mathematical and Theoretical, 50. doi:10.1088/1751-8121/aa6dc1