Orthogonal polynomials
Another connection between orthogonal polynomials and L-orthogonal polynomials
... Such polynomials were introduced in [7] in order to solve the strong Stieltjes moment ...of orthogonal Laurent polynomials or orthogonal L-polynomials associated with the measure ψ (see ...
19
Deformed Laguerre-Hahn orthogonal polynomials on the real line
... co-prime polynomials now de- pending on a parameter t (we consider a general ...corresponding orthogonal polynomials, as well as its recurrence relation coefficients, will also depend on ...
17
Discrete semi-classical orthogonal polynomials of class one on quadratic lattices
... semi-classical orthogonal polynomials of class one when D is the Hahn’s difference ...semi-classical orthogonal polynomials of class one when D is the forward difference ...
21
On differential equations for orthogonal polynomials on the unit circle
... of orthogonal poly- nomials on the unit circle are factorized in terms of well characterized semi- classical sequences of orthogonal ...semi-classical orthogonal polynomials on the unit ...
25
The Symmetric Semi-classical Orthogonal Polynomials of Class Two and Some of Their Extensions
... of orthogonal polynomials of class two related to Stieltjes functions satisfying a Riccati type differential equation with polynomial ...the orthogonal polynomials as well as for related ...
20
Classification of Laguerre-Hahn orthogonal polynomials of class one
... Laguerre-Hahn orthogonal poly- nomials, obtained trough the so-called compatibility conditions that result from combining the matrix Sylvester equation with the recurrence relation for the orthogonal ...
18
Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line
... (semi-classical) orthogonal polynomials showing its relevance in the theory of integrable systems and Painlev´e equa- tions, and we refer the reader to [13] and the references therein (see also ...
19
Laguerre-Hahn orthogonal polynomials on the real line
... of orthogonal polynomial solutions is known: the polynomials must be, up to a linear change of variable, a member of the clas- sical families, that is, the Hermite, Laguerre, Jacobi, and Bessel ...
37
Characterizations of Laguerre-Hahn affne orthogonal polynomials on the unit circle
... Laurent polynomials with complex coefficients was ...are polynomials (see, in sec- tion 3, the definition of the derivation operator D ), and the corresponding sequences of orthogonal ...
19
A characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices
... semi-classical orthogonal polynomials on snul via difference systems that involve the polynomials as well some related functions, the so-called functions of the second kind (see Section 2 for more ...
18
Differential equations for families of semi- classical orthogonal polynomials within class one
... In this paper we derived general differential equations for the recurrence re- lation coefficients of the semi-classical orthogonal polynomials of class one with an additional assumption that the degree of ...
22
On the semiclassical character of orthogonal polynomials satisfying structure relations
... A theme of research in the theory of orthogonal polynomials is the char- acterization of orthogonal polynomial sequences satisfying a given structure relation. In this issue we refer the reader to ...
28
Discrete Painlevé Equations for Recurrence Coefficients of Laguerre-Hahn Orthogonal Polynomials of Class One
... for orthogonal polynomials related to the differential equations of general type (1) is connected to a wide range of subjects in mathematics, such as probability theory [16], differential equations [22, ...
19
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
Structure relations for orthogonal polynomials on the unit circle
... Concerning orthogonality on the real line, a well-known topic of research in the literature is to establish the semi-classical character of sequences of orthogonal polynomials in terms of structure ...
19
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 ...nal polynomials (the “Riccati model”) in the study of the convergence of Jacobi continued ...Laguerre-Hahn orthogonal ...
24
Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions
... of orthogonal polynomials on systems of non-uniform lattices, that is, families of orthogonal polynomials for which the formal Stieltjes function satisfies a Riccati difference equation with ...
21
Szego polynomials: some relations to L-orthogonal and orthogonal polynomials
... Szeg˝o polynomials and obtain some relations to certain self inversive orthogonal L-polynomials de ned on the unit circle and corresponding symmetric orthogonal polynomials on real ...
10
Connection coefficients and zeros of orthogonal polynomials
... Doubtless, the main contribution to the third problem is the comprehensive article of Karlin and Szeg˝o [17] where variety of inequalities concerning Wronskians and Turanians associated with orthogonal ...
10
Chain sequences and symmetric generalized orthogonal polynomials
... One of the main contributors highlighting the importance of positive chain sequences in the theory of orthogonal polynomials is Chihara and many results on these chain sequences can be found in his book ...
12