Results 91 to 100 of about 351,291 (192)
On some asymptotic properties of classical Hermite polynomials modified by a rational factor
Revista Integración, 2018 In this paper we study some asymptotic properties of the sequence of monic polynomials orthogonal with respect to the measure dµ = x 2+a x2+b e −x 2 dx, where a, b > 0 and a 6= b.
Luis Alejandro Molano Molano
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Sobolev Freud polynomials [PDF]
arXiv, 2015 We investigate the uniform asymptotic of some Sobolev orthogonal polynomials. Three term recurrence relation is given, moreover we give a recurrence relation between the so-called Sobolev orthogonal polynomials and Freud orthogonal polynomials.
arxiv
Ladder operators and differential equations for multiple orthogonal polynomials [PDF]
, 2012 In this paper, we obtain the ladder operators and associated compatibility conditions for the type I and the type II multiple orthogonal polynomials. These ladder equations extend known results for orthogonal polynomials and can be used to derive the differential equations satisfied by multiple orthogonal polynomials.
arxiv +1 more source
Orthogonal polynomials and Möbius transformations [PDF]
arXiv, 2019 Given an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing these polynomials with a general M\"obius transformation. In this work, we study the properties of such M\"obius-transformed polynomials. We show that they satisfy an orthogonality relation in given curve of the complex plane with respect
arxiv
Orthogonal polynomials and Stieltjes functions: the Laguerre-Hahn case [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1996 In this paper we consider orthogonal polynomials of the so-called Laguerre-Hahn class. This means that the Stieltjes function associated with the corresponding moment sequence satisfies a Riccati differential equation with polynomial coefficients.
E. PRIANES, F. MARCELLÁN
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Rakhmanov's theorem for orthogonal matrix polynomials on the unit circle [PDF]
J. Approx. Theory 146 (2007), 227-242, 2006 Rakhmanov's theorem for orthogonal polynomials on the unit circle gives a sufficient condition on the orthogonality measure for orthogonal polynomials on the unit circle, in order that the reflection coefficients (the recurrence coefficients in the Szego recurrence relation) converge to zero.
arxiv
A note on semi-classical orthogonal polynomials [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 1996 We prove that one characterization for the classical orthogonal polynomials sequences (Hermite, Laguerre, Jacobi and Bessel) cannot be extended to the semi-classical ones.
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Results on the associated classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 1995 AbstractLet {Pk(x)} be any system of the classical orthogonal polynomials, and let {Pk(x; c)} be the corresponding associated polynomials of order c (c ∈ N). Second-order recurrence relation (in k) is given for the connection coefficient an−1,k(c) in Pn−1(x;c)=σk=0n−1 an−1,k(c)Pk(x).
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Ain Shams Engineering Journal, 2018 The theme of this paper is to analyze and compare the pulse compression with classical orthogonal polynomials (Chebyshev, Laguerre, Legendre and Hermite polynomials) of different orders.
Ankur Thakur, Salman Raju Talluri
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A Probablistic Origin for a New Class of Bivariate Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an ...
Michael R. Hoare, Mizan Rahman
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