Results 101 to 110 of about 351,291 (192)
On ( p , q ) $(p,q)$ -classical orthogonal polynomials and their characterization theorems
Advances in Difference Equations, 2017 In this paper, we introduce a general ( p , q ) $(p, q)$ -Sturm-Liouville difference equation whose solutions are ( p , q ) $(p, q)$ -analogues of classical orthogonal polynomials leading to Jacobi, Laguerre, and Hermite polynomials as ( p , q ) → ( 1 ...
M Masjed-Jamei +3 more
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Umbral "classical" polynomials [PDF]
arXiv, 2014 We study the umbral "classical" orthogonal polynomials with respect to a generalized derivative operator $\cal D$ which acts on monomials as ${\cal D} x^n = \mu_n x^{n-1}$ with some coefficients $\mu_n$. Let $P_n(x)$ be a set of orthogonal polynomials. Define the new polynomials $Q_n(x) =\mu_{n+1}^{-1}{\cal D} P_{n+1}(x)$.
arxiv
Krall--type Orthogonal Polynomials in several variables [PDF]
arXiv, 2007 For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional in several variables, explicit formulas of orthogonal polynomials are derived from the orthogonal polynomials associated with the moment functional. Explicit formula for the reproducing kernel is also derived and used to establish certain inequalities for ...
arxiv
Characterizations of classical orthogonal polynomials on quadratic lattices [PDF]
arXiv, 2016 This paper is devoted to characterizations classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal polynomials on quadratic lattices. Moreover a new characterization is also presented.
arxiv
A characterization of classical orthogonal Laurent polynomials
Indagationes Mathematicae (Proceedings), 1988 AbstractIn [3] certain Laurent polynomials of 2F1 genus were called “Jacobi Laurent polynomials”. These Laurent polynomials belong to systems which are orthogonal with respect to a moment sequence ((a)n/(c)n)nεℤ where a, c are certain real numbers. Together with their confluent forms, belonging to systems which are orthogonal with respect to 1/(c)n)nεℤ
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On the modifications of classical orthogonal polynomials: The symmetric case
Approximation Theory and its Applications, 1998 We consider the modifcations of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the origin. Some properties of the resulting polynomials are studied: three-term recurrence relation, differential equation, ratio asymptotics, hypergeometric representation as well as, for large n, the behaviour of their zeros.
Álvarez Nodarse, Renato +1 more
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Nice q-analogs of orthogonal polynomials with nice moments: Some simple examples [PDF]
arXivIn this note I collect some typical examples of orthogonal polynomials with simple moments where both moments and orthogonal polynomials have nice q-analogs.
arxiv
New Characterizations of Discrete Classical Orthogonal Polynomials
Journal of Approximation Theory, 1997 AbstractWe prove that if both {Pn(x)}∞n=0and {∇rPn(x)}∞n=rare orthogonal polynomials for any fixed integer r⩾1, then {Pn(x)}∞n=0must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahn's theorem stating that if both {Pn(x)}∞n=0and {(d/dx)rPn(x)}∞n=rare orthogonal polynomials, then {Pn(x)}∞n=0are ...
Kwon, KH Kwon, Kil Hyun +2 more
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The relativistic Laguerre polynomials [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1996 A new relativistic-type polynomial system is defined by means of the Relativistic Hermite Polynomial system, introduced recently by V.Aldaya et al. to express the wave functions of the quantum relativistic harmonic oscillator.
P. NATALINI
doaj
Alternative Orthogonal Polynomials [PDF]
arXiv, 2004 The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences that are the result of the inverse orthogonalization procedure.
arxiv