Results 41 to 50 of about 66,130 (225)
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 +3 more
openaire +2 more sources
Connection coefficients for classical orthogonal polynomials of several variables [PDF]
, 2015 Connection coefficients between different orthonormal bases satisfy two discrete orthogonal relations themselves. For classical orthogonal polynomials whose weights are invariant under the action of the symmetric group, connection coefficients between a ...
P. Iliev, Yuan Xu
semanticscholar +1 more source
Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions [PDF]
Transactions of the American Mathematical Society, 2019 The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settings involving either a linear or an exponential lattice. The corresponding correlation functions can be expressed in terms of
P. Forrester, Shi‐Hao Li
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
New Formulas and Connections Involving Euler Polynomials
Axioms, 2022 The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as well
Waleed Mohamed Abd-Elhameed +1 more
doaj +1 more source
On some classical type Sobolev orthogonal polynomials [PDF]
Journal of Approximation Theory, 2019 In this paper we propose a way to construct classical type Sobolev orthogonal polynomials. We consider two families of hypergeometric polynomials: ${}_2 F_2(-n,1;q,r;x)$ and ${}_3 F_2(-n,n-1+a+b,1;a,c;x)$ ($a,b,c,q,r>0$, $n=0,1,...$), which generalize ...
S. Zagorodnyuk
semanticscholar +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
Perturbations around the zeros of classical orthogonal polynomials [PDF]
, 2014 Starting from degree N solutions of a time dependent Schrodinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around the N zeros of the polynomial is derived.
R. Sasaki
semanticscholar +1 more source
Classical skew orthogonal polynomials in a two-component log-gas with charges +1 and +2 [PDF]
Advances in Mathematics, 2019 There is a two-component log-gas system with Boltzmann factor which provides an interpolation between the eigenvalue PDF for $\beta = 1$ and $\beta = 4$ invariant random matrix ensembles.
P. Forrester, Shi‐Hao Li
semanticscholar +1 more source