# Direct spreading measures of Laguerre polynomials

@article{SnchezMoreno2011DirectSM,
title={Direct spreading measures of Laguerre polynomials},
author={Pablo S{\'a}nchez-Moreno and Daniel Manzano and Jes{\'u}s S{\'a}nchez-Dehesa},
journal={ArXiv},
year={2011},
volume={abs/1009.0289}
}
• Published 1 September 2010
• Mathematics
• ArXiv

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## References

SHOWING 1-10 OF 87 REFERENCES
• Computer Science, Mathematics
J. Comput. Appl. Math.
• 2010
Information-theoretic lengths of Jacobi polynomials
• Mathematics
• 2010
The information-theoretic lengths of the Jacobi polynomials P(α, β)n(x), which are information-theoretic measures (Renyi, Shannon and Fisher) of their associated Rakhmanov probability density, are
Effective Laguerre Asymptotics
• Mathematics
SIAM J. Numer. Anal.
• 2008
A computationally motivated contour integral is introduced that allows efficient numerical Laguerre evaluations yet also leads to the complete asymptotic series over the full parameter domain of subexponential behavior.
Strong asymptotics of Laguerre polynomials and information entropies of two-dimensional harmonic oscillator and one-dimensional Coulomb potentials
• Physics
• 1998
The information entropies of the two-dimensional harmonic oscillator, V(x,y)=1/2λ(x2+y2), and the one-dimensional hydrogen atom, V(x)=−1/|x|, can be expressed by means of some entropy integrals of
Entropic functionals of Laguerre polynomials and complexity properties of the half-line Coulomb potential
• Computer Science
• 2009
The Shannon entropy and the LMC shape complexity of the lowest and highest (Rydberg) energetic states are explicitly given; moreover, sharp information-theoretic-based upper bounds to these quantities are found for general physical states.
Linearization of arbitrary products of classical orthogonal polynomials
• Mathematics
• 2000
A procedure is proposed in order to expand w = ∏N j=1 Pij (x) = ∑M k=0 LkPk(x) where Pi(x) belongs to a classical orthogonal polynomial sequence (Jacobi, Bessel, Laguerre and Hermite) (M = ∑N j=1
Clebsch-Gordan-type linearisation relations for the products of Laguerre polynomials and hydrogen-like functions
Two series of Clebsch-Gordan type linearisation relations are derived for the most general product of the Laguerre polynomials, Ln1alpha 1(u1x)Ln2alpha 2(u2x), which differ in orders, n, weights,