We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and center-of-mass motions. A general expression for the relative Wigner function is obtained in terms of the Laguerre polynomials by introducing a new identity ...

In this paper we present a connection between systems of differential equations for the recurrence coefficients polynomials orthogonal with respect to generalized Meixner and deformed Laguerre weights. It is well-known that both can be expressed in terms solutions fifth Painlevé equation but no explicit relation was known. We also certain limits which XXXIV equation, case extends previous studi...

We derive analytical formulae for the complex amplitudes of variants generalized Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams. reveal that, at particular values parameters exact solution paraxial propagation equation, these beams are converted into conventional elegant HG LG also deduce asymmetric that described by in form Hermite Laguerre polynomials whose argument is shifted plane. ...

The Cholesky factorization of the moment matrix is applied to discrete orthogonal polynomials on homogeneous lattice. In particular, semiclassical polynomials, which are built in terms a Pearson equation, studied. Laguerre–Freud structure semiinfinite that models shifts by ±1 independent variable set introduced. case it proven this banded. From well-known fact moments weights logarithmic deriva...

Abstrakt This article deals with the use of the Laguerre functions in the data compression. After the short introduction the definition of the Laguerre polynomials and functions is given. The application of the discrete Laguerre transform on the data compression is shown. It is pointed out that the discrete Laguerre transform can give better results than the discrete cosine transform in the tas...

The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite, Laguerre and Jacobi polynomials. The eigenfunctions of the corresponding single-particle quantum CSM systems are also expressed in terms of the same ...

This paper develops and compares specification tests for parametric duration models estimated with censored data. The tests are based on generalized residuals (the integrated hazard), which is exponentially distributed if the model is correctly specified. I present several conditional moment tests based on the generalized residuals: a raw moments test, a test based on Laguerre polynomials, and ...

Abstract. Through an algebraic method using the Dunkl–Cherednik operators, the multivariable Hermite and Laguerre polynomials associated with the AN−1and BN Calogero models with bosonic, fermionic and distinguishable particles are investigated. The Rodrigues formulas of column type that algebraically generate the monic nonsymmetric multivariable Hermite and Laguerre polynomials corresponding to...

In this paper, we show that the sum rules for generalized Hermite polynomials derived by Daboul and Mizrahi (2005 J. Phys. A: Math. Gen. 38 427–48) and by Graczyk and Nowak (2004 C. R. Acad. Sci., Ser. 1 338 849) can be interpreted and easily recovered using a probabilistic moment representation of these polynomials. The covariance property of the raising operator of the harmonic oscillator, wh...

A brain tumor occurs when abnormal cells form within the brain. Glioblastoma (GB) is an aggressive and fast-growing type of that invades tissue or spinal cord. GB evolves from astrocytic glial in central nervous system. can occur at almost any age, but occurrence increases with advancing age older adults. Its symptoms may include nausea, vomiting, headaches, even seizures. GB, formerly known as...