Results 21 to 30 of about 978,477 (364)
Generalizations of orthogonal polynomials [PDF]
Journal of Computational and Applied Mathematics, 2005 The paper is a clearly written survey. The following generalizations of orthogonal polynomials are considered: orthogonal rational functions; homogeneous multivariate orthogonal polynomials; vector and matrix orthogonal polynomials; multiple orthogonal polynomials.
Bultheel, A. +4 more
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Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]
, 2013 Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
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Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators [PDF]
, 2016 We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types.
S. Odake
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Journal of Approximation Theory, 1979 Abstract : Orthogonal polynomials satisfy a three term recurrence relation. The purpose of the paper is to give estimates for the orthogonal polynomials and the corresponding weight function provided that the coefficients in the recurrence formula behave in a prescribed manner. (Author)
Paul Nevai, Paul Nevai
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Some Orthogonal Polynomials Arising from Coherent States [PDF]
, 2011 We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature.
Akhiezer N I +19 more
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Zernike polynomials and their applications
Journal of Optics, 2022 The Zernike polynomials are a complete set of continuous functions orthogonal over a unit circle. Since first developed by Zernike in 1934, they have been in widespread use in many fields ranging from optics, vision sciences, to image processing. However,
Kuo Niu, Chao Tian
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Orthogonal Polynomials On Ellipses And Their Recurrence Relations
Demonstratio Mathematica, 2014 In this note we study the connection between orthogonal polynomials on an ellipse and orthogonal Laurent polynomials on the unit circle relative to some multiplicative measures and then establish the recurrence relations for orthogonal polynomials on an ...
Lauric Vasile
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Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy [PDF]
, 2015 Given a matrix polynomial $W(x)$, matrix bi-orthogonal polynomials with respect to the sesquilinear form $\langle P(x),Q(x)\rangle_W=\int P(x) W(x)\operatorname{d}\mu(x)(Q(x))^{\top}$, $P(x),Q(x)\in\mathbb R^{p\times p}[x]$, where $\mu(x)$ is a matrix of
Carlos 'Alvarez-Fern'andez +4 more
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Orthogonal polynomials with orthogonal derivatives [PDF]
Bulletin of the American Mathematical Society, 1938 We are concerned with the following assertion: THEOREM. If {φn(x)} and { φn’(x)} are orthogonal systems of polynomials, then {φn(x)} may be reduced to the classical polynomials of Jacobi, Laguerre, or Hermite by means of a linear transformation on x.
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