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Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations

Communications, 2010
In applications of mathematics involving either the Laplace or the Helmholtz equation in spherical coordinates the associated Legendre equation occurs. Its solutions are called associated Legendre functions. They have some relations to classical Legendre
Vladimir Guldan, Mariana Marcokova
doaj   +1 more source

SECOND STRUCTURE RELATION FOR THE DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS

Проблемы анализа, 2023
In this paper, we characterize the Dunkl-classical orthogonal polynomials by a second structure relation.
Y. Habbachi
doaj   +1 more source

On 2-orthogonal polynomials of Laguerre type

International Journal of Mathematics and Mathematical Sciences, 1999
Let {Pn}n≥0 be a sequence of 2-orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let {Qn}n≥0 be the sequence of polynomials defined by Qn:=(n+1)−1P′n+1,n≥0.
Khalfa Douak
doaj   +1 more source

An example of nonsymmetric semi-classical form of class s=1; generalization of a case of Jacobi sequence

International Journal of Mathematics and Mathematical Sciences, 2000
We give explicitly the recurrence coefficients of a nonsymmetric semi-classical sequence of polynomials of class s=1. This sequence generalizes the Jacobi polynomial sequence, that is, we give a new orthogonal sequence {Pˆn(α,α+1)(x,μ)}, where μ is an ...
Mohamed Jalel Atia
doaj   +1 more source

A Dunkl-classical d-symmetric d-orthogonal polynomial set [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 2010
In this paper, we apply a d-orthogonality preserving operator to the Humbert polynomials to derive a new Dunkl-classical d-orthogonal polynomials generalizing the Humbert ones.
Y. Ben Cheikh, M. Gaied
doaj  

Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials

Mathematics, 2019
In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials.
Dae San Kim, Dmitry V. Dolgy, Dojin Kim, Taekyun Kim   +3 more
doaj   +1 more source

A NOTE FOR THE DUNKL-CLASSICAL POLYNOMIALS

Проблемы анализа, 2022
In this paper, we give a new characterization for the Dunkl-classical orthogonal polynomials. The previous characterization has been illustrated by some examples.
Y. Habbachi, B. Bouras
doaj   +1 more source

On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials [PDF]

Journal of difference equations and applications (Print), 2020
For every system of OPRL or OPUC, we construct Sobolev orthogonal polynomials , with explicit integral representations involving . Two concrete families of Sobolev orthogonal polynomials (depending on an arbitrary number of complex parameters) which are ...
S. Zagorodnyuk
semanticscholar   +1 more source

Determinant inequalities for sieved ultraspherical polynomials

International Journal of Mathematics and Mathematical Sciences, 2001
Paul Turan first observed that the Legendre polynomials satisfy the inequality Pn2(x)−Pn−1(x)Pn(x)>0 ...
J. Bustoz, I. S. Pyung
doaj   +1 more source

On an system of “classical” polynomials of simultaneous orthogonality

Journal of Computational and Applied Mathematics, 1996
AbstractWe introduce a system of “classical” polynomials of simultaneous orthogonality, study the differential equation of third order, recurrence relation and precise the ratio asymptotic and zeros distribution of polynomials.
André Ronveaux, V. Kaliaguine
openaire   +3 more sources