نتایج جستجو برای: laguerre polynomials

تعداد نتایج: 39597  

2016
Mongi BLEL

In this work, we give a unification and generalization of Laguerre and Hermite polynomials for which the orthogonal property is replaced by the d-orthogonality. We state some properties of these new polynomials. 2010 Mathematics Subject Classification: Primary 42C05, 33C45, 33C20.

Journal: :Research in number theory 2021

Abstract Horizontal and vertical generating functions recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal log-concavity of sequences assigned to polynomials which show up in combinatorics, number theory physics. This includes Laguerre polynomials, Pochhammer D’Arcais Nekrasov–Okounkov polynomials.

2008
Michael Filaseta Travis Kidd Ognian Trifonov

In 1892, D. Hilbert began what is now called Inverse Galois Theory by showing that for each positive integer m, there exists a polynomial of degree m with rational coefficients and associated Galois group Sm, the symmetric group on m letters, and there exists a polynomial of degree m with rational coefficients and associated Galois group Am, the alternating group on m letters. In the late 1920’...

2008
FREDERIC UTZET

Given a stochastic process X = {Xt, t ∈ R+} with finite moments of convenient order, a time–space harmonic polynomial relative to X is a polynomial Q(x, t) such that the process Mt =Q(Xt, t) is a martingale with respect to the filtration associated with X . Major examples are the Hermite polynomials relative to a Brownian motion, the Charlier polynomials relative to a Poisson process and the La...

1999
Peter Borwein Tamás Erdélyi John Zhang JOHN ZHANG

The Müntz–Legendre polynomials arise by orthogonalizing the Müntz system {xλ0 , xλ1 , . . . } with respect to the Lebesgue measure on [0, 1]. In this paper, differential and integral recurrence formulas for the Müntz–Legendre polynomials are obtained. Interlacing and lexicographical properties of their zeros are studied, and the smallest and largest zeros are universally estimated via the zeros...

Journal: :J. Symb. Comput. 2007
Ioana Dumitriu Alan Edelman Gene Shuman

In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also compute multivariate hypergeometric functions, and offer both symbolic and numerical evaluations for all these quantities. We prove that all algorithms are wel...

2018
FELIPE GONÇALVES

Orthogonal polynomials have been used to produce sharp estimates in Harmonic Analysis in several instances. The first most notorious and original use was in Beckner’s thesis [1], where he proved the sharp Hausdorff-Young inequality using Hermite polynomial expansions. More recently, Foschi [4] used spherical harmonics and Gegenbauer polynomials in his proof of the sharp Tomas-Stein adjoint Four...

2009
K. Parand M. Shahini A. Taghavi

In this paper we propose, a collocation method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semiinfnite interval. This approach is based on generalized Laguerre polynomials and rational Chebyshev functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with...

Journal: :Acta Arithmetica 2021

Inspired by the work of Schur on Taylor series exponential and Laguerre polynomials, we study Galois theory trimmed exponentials $f_{n,n+k}=\sum _{i=0}^{k} {x^{i}/(n+i)!}$ generalized polynomials $L^{(n)}_k$ degree

2011
Pradipto Banerjee Michael Filaseta Carrie E. Finch Russell Leidy

We show that the discriminant of the generalized Laguerre polynomial L n (x) is a non-zero square for some integer pair (n, α), with n ≥ 1, if and only if (n, α) belongs to one of 30 explicitly given infinite sets of pairs or to an additional finite set of pairs. As a consequence, we obtain new information on when the Galois group of L n (x) over Q is the alternating group An. For example, we e...

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