Results 31 to 40 of about 58,842 (311)

Nearest Neighbor Recurrence Relations for Meixner–Angelesco Multiple Orthogonal Polynomials of the Second Kind

Mathematics, 2023
This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set.
Jorge Arvesú, Alejandro J. Quintero Roba   +1 more
doaj   +1 more source

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

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

Characterization of classical type orthogonal polynomials [PDF]

Proceedings of the American Mathematical Society, 1994
We characterize the classical type orthogonal polynomials { P n ( x ) } 0 ∞ \{ {P_n}(x)\} _0^\infty satisfying a fourth-order differential equation of type \[ ∑ i
KWON, KH Kwon, Kil Hyun, LITTLEJOHN, LL, LEE, JK, YOO, BH   +3 more
openaire   +2 more sources

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

CHARACTERIZATION OF POLYNOMIALS VIA A RAISING OPERATOR

Проблемы анализа, 2023
This paper investigates a first-order linear differential operator 𝒥𝜉, where 𝜉 = (𝜉1, 𝜉2)\in (C^2\(0,0), and 𝐷 := 𝑑/𝑑𝑥. The operator is defined as 𝒥𝜉 := 𝑥(𝑥𝐷+ I) + 𝜉1 I + 𝜉2𝐷, with I representing the identity on the space of polynomials with complex ...
Jihad Souissi
doaj   +1 more source