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}
}

Figures and Tables from this paper

Complexity analysis of hypergeometric orthogonal polynomials
Information-theoretic lengths of Jacobi polynomials
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
Linearization and Krein-like functionals of hypergeometric orthogonal polynomials
The Krein-like $r$-functionals of the hypergeometric orthogonal polynomials $\{p_{n}(x) \}$ with kernel of the form $x^{s}[\omega(x)]^{\beta}p_{m_{1}}(x)\ldots p_{m_{r}}(x)$, being $\omega(x)$ the
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 of the main entropy-like measures of their associated Rakhmanov’s
Complexity-like properties and parameter asymptotics of Lq -norms of Laguerre and Gegenbauer polynomials
The main monotonic statistical complexity-like measures of the Rakhmanov’s probability density associated to the hypergeometric orthogonal polynomials (HOPs) in a real continuous variable, each of
A ug 2 02 1 Complexity-like properties and parameter asymptotics of L q-norms of Laguerre and Gegenbauer polynomials
The main monotonic statistical complexity-like measures of the Rakhmanov’s probability density associated to the hypergeometric orthogonal polynomials (HOPs) in a real continuous variable, each of
Frequency moments, $$L_{q}$$Lq norms and Rényi entropies of general hypergeometric polynomials
The basic variables of the information theory of quantum systems (e.g., frequency or entropic moments, Rényi and Tsallis entropies) can be expressed in terms of $$L_{q}$$Lq norms of general
Information-Theoretic-Based Spreading Measures of Orthogonal Polynomials
The macroscopic properties of a quantum system strongly depend on the spreading of the physical eigenfunctions (wavefunctions) of its Hamiltonian operador over its confined domain. The wavefunctions
Wehrl entropies and Euclidean Landau levels
We are concerned with an information-theoretic measure of uncertainty for quantum systems. Precisely, the Wehrl entropy of the phase-space probability $Q^{(m)}_{\hat{\rho}}=\left\langle
...
1
2
3
...

References

SHOWING 1-10 OF 87 REFERENCES
Spreading lengths of Hermite polynomials
Information-theoretic lengths of Jacobi polynomials
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
TLDR
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
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
TLDR
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
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,
...
1
2
3
4
5
...