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arXiv · 1705.03627

Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters

N. M. Temme·I. V. Toranzo·J. S. Dehesa
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Abstract

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 ($\mathcal{L}_{m}^{(α)}(x)$) and Gegenbauer ($\mathcal{C}^{(α)}_{m}(x)$) polynomials in both position and momentum spaces, where the parameter $α$ linearly depends on $D$. In this work we study the asymptotic behavior as $α\to \infty$ of the associated entropy-like integral functionals of these two families of hypergeometric polynomials.

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N. M. Temme, I. V. Toranzo, J. S. Dehesa. 2017-05-10. Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters. https://doi.org/10.1088/1751-8121%2Faa6dc1

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