Results 1 to 10 of about 66,130 (225)

Classical orthogonal polynomials: dependence of parameters

Journal of Computational and Applied Mathematics, 2000
The authors study connection problems between classical orthogonal polynomials and their derivatives with respect to (one of) their parameter(s). They use their so-called \texttt{Navima} algorithm to derive recurrence relations for the connection coefficients linking a family of classical orthogonal polynomials (like the Laguerre and Jacobi polynomials)
Ronveaux, André, Zarzo, A., Area, I., Godoy, E.   +3 more
openaire   +2 more sources

On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices

Bulletin of Mathematical Sciences
Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation.
Misael E. Marriaga, Guillermo Vera de Salas, Marta Latorre, Rubén Muñoz Alcázar   +3 more
doaj   +1 more source

Zero distribution of sequences of classical orthogonal polynomials

Abstract and Applied Analysis, 2003
We obtain the zero distribution of sequences of classical orthogonal polynomials associated with Jacobi, Laguerre, and Hermite weights. We show that the limit measure is the extremal measure associated with the corresponding weight.
Plamen Simeonov
doaj   +1 more source

The Laguerre Constellation of Classical Orthogonal Polynomials

Mathematics
A linear functional u is classical if there exist polynomials ϕ and ψ with degϕ≤2 and degψ=1 such that Dϕ(x)u=ψ(x)u, where D is a certain differential, or difference, operator. The polynomials orthogonal with respect to the linear functional u are called
Roberto S. Costas-Santos
doaj   +1 more source

A characterization of the four Chebyshev orthogonal families

International Journal of Mathematics and Mathematical Sciences, 2005
We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear ...
E. Berriochoa, A. Cachafeiro, J. M. Garcia-Amor   +2 more
doaj   +1 more source

Complementary Romanovski-Routh polynomials and their zeros

Trends in Computational and Applied Mathematics
The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials.
L. L. Silva Ribeiro, A. Sri Ranga, Yen Chi Lun   +2 more
doaj   +1 more source

Invariance properties of Wronskian type determinants of classical and classical discrete orthogonal polynomials

Journal of Mathematical Analysis and Applications, 2019
Given a finite set F = { f 1 , ⋯ , f k } of nonnegative integers (written in increasing order of magnitude) and a classical discrete family ( p n ) n of orthogonal polynomials (Charlier, Meixner, Krawtchouk or Hahn), we consider the Casorati determinant ...
G. Curbera, A. J. Durán
semanticscholar   +1 more source

Tridiagonal Operators and Zeros of Polynomials in Two Variables

Abstract and Applied Analysis, 2016
The aim of this paper is to connect the zeros of polynomials in two variables with the eigenvalues of a self-adjoint operator. This is done by use of a functional-analytic method.
Chrysi G. Kokologiannaki, Eugenia N. Petropoulou, Dimitris Rizos   +2 more
doaj   +1 more source

The Spectral Connection Matrix for Any Change of Basis within the Classical Real Orthogonal Polynomials

Mathematics, 2015
The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
doaj   +1 more source

Discriminants of classical quasi-orthogonal polynomials with application to Diophantine equations

Journal of the Mathematical Society of Japan, 2019
We derive explicit formulas for the discriminants of classical quasi-orthogonal polynomials, as a full generalization of the result of Dilcher and Stolarsky (2005).
M. Sawa, Y. Uchida
semanticscholar   +1 more source