Laguerre-Hahn orthogonal polynomials
Classification of Laguerre-Hahn orthogonal polynomials of class one
... for Laguerre-Hahn orthogonal polynomials to be used throughout the paper, and we discuss some remarks on the canonical forms of Laguerre-Hahn functional equations; in Section 3 ...
18
Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line
... In subsection 5.1 we will show the solutions of the corresponding difference equation (15) in the class zero: we give closed form expressions for the recur- rence relation coefficients of the orthogonal ...
19
Laguerre-Hahn orthogonal polynomials on the real line
... of orthogonal polynomials with discrete Painlev´ e equations is a well-known subject, much analysis has been carried out within the families of orthogonal polynomials related to semi-classical ...
37
Discrete Painlevé Equations for Recurrence Coefficients of Laguerre-Hahn Orthogonal Polynomials of Class One
... of Laguerre-Hahn orthogonal polynomials in class one ...of orthogonal polynomials remains ...of orthogonal polynomials belonging to Laguerre-Hahn ...
19
Deformed Laguerre-Hahn orthogonal polynomials on the real line
... Connection with semi-classical orthogonal polynomials: the use of Radon’s Lemma. In what follows we establish a relation between H n and a matrix (to be specified through the text) related to semi-classical ...
17
On linear spectral transformations and the Laguerre-Hahn class
... for Laguerre-Hahn orthogonal polynomials on the real ...of orthogonal polynomials and the consequences for the three-term recur- rence relation ...
21
Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions
... for Laguerre-Hahn orthogonal polynomials on systems of non-uniform lattices, the so-called compatibility con- ditions, involving the transfer ...the Laguerre-Hahn ...
21
Second- order differential equations in the Laguerre-Hahn class
... the Laguerre-Hahn orthogonal polynomials are a generalization of the semi-classical orthogonal polynomials, since the later ones are related to (3) with B ≡ 0, the classical ...
26
Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle
... with orthogonal polynomials on the unit circle and also on the real ...and Hahn [15, 16]. In [18] Magnus used the theory of Laguerre-Hahn orthogo- nal polynomials (the “Riccati ...
24
The Symmetric Semi-classical Orthogonal Polynomials of Class Two and Some of Their Extensions
... of Laguerre-Freud equations for Laguerre-Hahn orthogonal poly- nomials has been done for several instances of the polynomials A, B, C, D in (3) (see [1, 7, 14, 15, ...
20
On differential equations for orthogonal polynomials on the unit circle
... such polynomials (equivalently, the set of such Carath´eodory func- tions) was defined in [3, 4] as the Laguerre-Hahn class on the unit ...the Laguerre- Hahn affine class on the unit ...
25
Characterizations of Laguerre-Hahn affne orthogonal polynomials on the unit circle
... C polynomials (cf. [11]). It is known that the Laguerre-Hahn affine class and the semi-classical class ...is Laguerre-Hahn affine if, and only if, u satisfies a functional Pearson ...
19
Differential equations for families of semi- classical orthogonal polynomials within class one
... the Laguerre-Hahn class ...of Laguerre-Hahn polynomials, for instance in the case of the associated poly- nomials, there will also be a connection to the Painlev´ e ...
22
Comportamento assintótico dos polinômios ortogonais de Sobolev-Jacobi e Sobolev-Laguerre
... de Laguerre (α = 0) já aparecem nos trabalhos de Niels Henrink Abel (1802-1829), Joseph-Louis Lagrange (1736-1813) e Chebyshev [15], antes mesmo de Edmond Nicolas Laguerre (1834-1886) estudá-los em 1875 ...
94
Discrete semi-classical orthogonal polynomials of class one on quadratic lattices
... Note that D has the following property: if f (x) is a polynomial of degree n in x, then Df (x) is a polynomial of degree n − 1 in x. Mf is a polynomial whenever f is a polynomial. Furthermore, if deg(f ) = n, then deg(Mf ...
21
Maria Gabriela Campolina Diniz Peixoto (1) , Daniel Jordan de Abreu Santos (2) , Rusbel Raul Aspilcueta Borquis (2), Frank Ângelo Tomita Bruneli (1) , João Cláudio do Carmo Panetto (1) and Humberto Tonhati (2)
... Legendre polynomials and reported the same tendency of the estimates (El Faro & Albuquerque ...Legendre polynomials and to the lower number of ...
12
Symmetric semi-classical orthogonal polynomials of class one on q-quadratic lattices
... 2.1. The General Divided Difference Operator, q-Quadratic Lat- tices, and Orthogonal Polynomials. We consider the divided difference operator D given in [ 10 , Eq.(1.1)], with the property that D leaves a ...
12
On Global Solution of Incompressible Navier-Stokes Equations
... Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of velocities for incompressible fluid in 1D, 2D and 3D space for ...
4
Modelo de Minkwoski para a Geometria de Laguerre
... Conv´em recordar que, quando usamos o termo ponto, nos referimos a um deter- minado ponto P do espa¸co de Minkowski. Fixado um plano euclidiano, esse mesmo ponto representa, no quadro da geometria de Laguerre, um ...
24
Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
... were obtained via the ladder operator scheme in [6] and add new equations via the above mentioned Laguerre method. Such equations are commonly known as Laguerre-Freud equations [12]. The main objective is ...
15