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2014, Second edition., Encyclopedia of mathematics and its applications, ISBN 1107071895, Volume 155, xvii, 420

.... It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains...

Functions of several real variables | Orthogonal polynomials

Functions of several real variables | Orthogonal polynomials

Book

Physics letters. B, ISSN 0370-2693, 02/2010, Volume 684, Issue 2-3, pp. 173 - 176

...) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials in one-dimensional quantum mechanics and the corresponding Xℓ...

Shape invariance | Orthogonal polynomials | Physical Sciences | Physics, Nuclear | Astronomy & Astrophysics | Physics, Particles & Fields | Physics | Science & Technology

Shape invariance | Orthogonal polynomials | Physical Sciences | Physics, Nuclear | Astronomy & Astrophysics | Physics, Particles & Fields | Physics | Science & Technology

Journal Article

2007, Annals of mathematics studies, ISBN 0691127344, Volume n. 164, vi, 170

This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set...

Orthogonal polynomials | Asymptotic theory | Mathematics | Polynomials

Orthogonal polynomials | Asymptotic theory | Mathematics | Polynomials

Book

4.
Szegö's theorem and its descendants

: spectral theory for L2 perturbations of orthogonal polynomials

2011, Porter Lectures, ISBN 0691147043, x, 650

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives...

Orthogonal polynomials | Spectral theory (Mathematics) | Spectral theory

Orthogonal polynomials | Spectral theory (Mathematics) | Spectral theory

Book

2014, Memoirs of the American Mathematical Society, ISBN 9781470416669, Volume no. 1091., v, 112

Book

Letters in mathematical physics, ISSN 0377-9017, 07/2018, Volume 108, Issue 7, pp. 1623 - 1634

.... A connection with the characterization of the little -1 Jacobi polynomials is found in the holomorphic realization of osp (1, 2...

Bannai–Ito algebra | Integral representations | Orthogonal polynomials | Quantum groups | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Algebra | Embedding | Polynomials | Mathematical analysis | Mathematical Physics | Mathematics

Bannai–Ito algebra | Integral representations | Orthogonal polynomials | Quantum groups | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Algebra | Embedding | Polynomials | Mathematical analysis | Mathematical Physics | Mathematics

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 11/2017, Volume 455, Issue 2, pp. 1801 - 1821

We consider orthogonal polynomials via polynomial mappings in the framework of the semiclassical class...

Moment linear functionals | Integral representations | Polynomial mappings | Classical and semiclassical orthogonal polynomials | Orthogonal polynomials | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Moment linear functionals | Integral representations | Polynomial mappings | Classical and semiclassical orthogonal polynomials | Orthogonal polynomials | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

2020, Tutorials, Schools, and Workshops in the Mathematical Sciences, ISBN 3030367436, 683

...) and also from other local universities in the domain of orthogonal polynomials and applications...

eBook

12/2017, Australian Mathematical Society Lecture Series, ISBN 9781108441940, Volume 27, 193

There are a number of intriguing connections between Painlevé equations and orthogonal polynomials, and this book is one of the first to provide an introduction...

Painleve equations | Polynomials | Differential equations, Nonlinear | Orthogonal polynomials

Painleve equations | Polynomials | Differential equations, Nonlinear | Orthogonal polynomials

eBook

Advances in applied mathematics, ISSN 0196-8858, 07/2016, Volume 78, pp. 56 - 75

The aim of this paper is the study of q−1-Fibonacci polynomials with 0

N-extremal measures | Measure of orthogonality | Orthogonal polynomials | q-sine | q-cosine | q-exponential | q-Fibonacci polynomials

Journal Article

Advances in difference equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 17

...)-analogues of classical orthogonal polynomials leading to Jacobi, Laguerre, and Hermite polynomials as (p, q).( 1, 1...

(p, q) -difference operators | (p, q) -Sturm-Liouville problems | (p, q) -classical orthogonal polynomials | (p, q) -integrals | (p, q) -Pearson difference equation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Theorems (Mathematics) | Usage | Polynomials | Difference equations | Tests, problems and exercises | Theorems | Hermite polynomials | ( p , q ) $(p,q)$ -integrals | ( p , q ) $(p,q)$ -classical orthogonal polynomials | ( p , q ) $(p,q)$ -Pearson difference equation | ( p , q ) $(p,q)$ -Sturm-Liouville problems | ( p , q ) $(p,q)$ -difference operators

(p, q) -difference operators | (p, q) -Sturm-Liouville problems | (p, q) -classical orthogonal polynomials | (p, q) -integrals | (p, q) -Pearson difference equation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Theorems (Mathematics) | Usage | Polynomials | Difference equations | Tests, problems and exercises | Theorems | Hermite polynomials | ( p , q ) $(p,q)$ -integrals | ( p , q ) $(p,q)$ -classical orthogonal polynomials | ( p , q ) $(p,q)$ -Pearson difference equation | ( p , q ) $(p,q)$ -Sturm-Liouville problems | ( p , q ) $(p,q)$ -difference operators

Journal Article

05/2016, Cambridge studies in advanced mathematics, ISBN 1107106982, Volume 153, 469

... hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including...

Functions, Special | Mathematical analysis | Orthogonal polynomials

Functions, Special | Mathematical analysis | Orthogonal polynomials

eBook

Journal of computational and applied mathematics, ISSN 0377-0427, 01/2013, Volume 237, Issue 1, pp. 83 - 101

.... Sanz-Serna, On polynomials orthogonal with respect to certain Sobolev inner products, J. Approx. Theory 65(2) (1991) 151–175...

Coherent pairs of measures | Moment linear functionals | Algorithms | Semiclassical orthogonal polynomials | Sobolev orthogonal polynomials | Orthogonal polynomials | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Integers | Functionals | Computation | Mathematical analysis | Coherence | Mathematical models | INT

Coherent pairs of measures | Moment linear functionals | Algorithms | Semiclassical orthogonal polynomials | Sobolev orthogonal polynomials | Orthogonal polynomials | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Integers | Functionals | Computation | Mathematical analysis | Coherence | Mathematical models | INT

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 04/2015, Volume 424, Issue 1, pp. 361 - 384

Given a sequence of polynomials (pn)n, an algebra of operators A that acts in the linear space of polynomials and an operator Dp∈A with Dp(pn)=θnpn, where θ...

Hahn polynomial | Krall polynomial | Difference operators and equations | Orthogonal polynomial | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Algebra

Hahn polynomial | Krall polynomial | Difference operators and equations | Orthogonal polynomial | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Algebra

Journal Article

Journal of approximation theory, ISSN 0021-9045, 02/2020, Volume 250, p. 105324

We investigate the type I and type II multiple orthogonal polynomials on an r-star with weight function |x|βe−xr, with β>−1. Each measure μj, for 1≤j...

Jacobi–Angelesco polynomials | Laguerre–Angelesco polynomials | Recurrence relation | Differential equation | Asymptotic zero distribution | Multiple orthogonal polynomials | Physical Sciences | Mathematics | Science & Technology | Mathematics - Classical Analysis and ODEs

Jacobi–Angelesco polynomials | Laguerre–Angelesco polynomials | Recurrence relation | Differential equation | Asymptotic zero distribution | Multiple orthogonal polynomials | Physical Sciences | Mathematics | Science & Technology | Mathematics - Classical Analysis and ODEs

Journal Article

Annals of physics, ISSN 0003-4916, 08/2013, Volume 335, pp. 78 - 85

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects...

Group representation theory | Quantum mechanics | Coherent states | Orthogonal polynomials | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Algebra | Polynomials | Lie groups | Functions (mathematics) | Mathematical analysis | Coherence | Differential equations | Hermite polynomials | Standards | Hilbert space | DIFFERENTIAL EQUATIONS | INTEGRAL CALCULUS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | EIGENSTATES | MATRIX ELEMENTS | QUANTUM MECHANICS | HILBERT SPACE | LEGENDRE POLYNOMIALS | RECURSION RELATIONS | HERMITE POLYNOMIALS | ANNIHILATION OPERATORS | LIE GROUPS

Group representation theory | Quantum mechanics | Coherent states | Orthogonal polynomials | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Algebra | Polynomials | Lie groups | Functions (mathematics) | Mathematical analysis | Coherence | Differential equations | Hermite polynomials | Standards | Hilbert space | DIFFERENTIAL EQUATIONS | INTEGRAL CALCULUS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | EIGENSTATES | MATRIX ELEMENTS | QUANTUM MECHANICS | HILBERT SPACE | LEGENDRE POLYNOMIALS | RECURSION RELATIONS | HERMITE POLYNOMIALS | ANNIHILATION OPERATORS | LIE GROUPS

Journal Article

Physics letters. B, ISSN 0370-2693, 08/2009, Volume 679, Issue 4, pp. 414 - 417

...–Teller potentials in terms of their degree ℓ polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (ℓ=1,2...

Shape invariance | Orthogonal polynomials | Physical Sciences | Physics, Nuclear | Astronomy & Astrophysics | Physics, Particles & Fields | Physics | Science & Technology

Shape invariance | Orthogonal polynomials | Physical Sciences | Physics, Nuclear | Astronomy & Astrophysics | Physics, Particles & Fields | Physics | Science & Technology

Journal Article

Journal of mathematical imaging and vision, ISSN 1573-7683, 09/2017, Volume 60, Issue 3, pp. 285 - 303

Krawtchouk polynomials (KPs) and their moments are used widely in the field of signal processing for their superior discriminatory properties...

Propagation error | Krawtchouk polynomial | Mathematical Methods in Physics | Signal,Image and Speech Processing | Computer Science | Image Processing and Computer Vision | Orthogonal polynomials | Signal processing | Krawtchouk moments | Applications of Mathematics | Physical Sciences | Technology | Computer Science, Artificial Intelligence | Mathematics | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Electrical engineering | Algorithms | Recursive algorithms | Face recognition | Computer simulation | Triangles | Coefficients | Image reconstruction | Partitions | Computation | Feature extraction | Polynomials | Symmetry

Propagation error | Krawtchouk polynomial | Mathematical Methods in Physics | Signal,Image and Speech Processing | Computer Science | Image Processing and Computer Vision | Orthogonal polynomials | Signal processing | Krawtchouk moments | Applications of Mathematics | Physical Sciences | Technology | Computer Science, Artificial Intelligence | Mathematics | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Electrical engineering | Algorithms | Recursive algorithms | Face recognition | Computer simulation | Triangles | Coefficients | Image reconstruction | Partitions | Computation | Feature extraction | Polynomials | Symmetry

Journal Article

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