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" Classical Orthogonal Polynomials of a Discrete Variable "
by Arnold F. Nikiforov, Vasilii B. Uvarov, Sergei K. Suslov.
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BL
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| Record Number
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753353
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b573314
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| Main Entry
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by Arnold F. Nikiforov, Vasilii B. Uvarov, Sergei K. Suslov.
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| Title & Author
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Classical Orthogonal Polynomials of a Discrete Variable\ by Arnold F. Nikiforov, Vasilii B. Uvarov, Sergei K. Suslov.
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| Publication Statement
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Berlin, Heidelberg : Springer Berlin Heidelberg, 1991
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| Series Statement
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Springer series in computational physics.
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| Page. NO
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(xvi, 374 pages 26 illustrations)
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| ISBN
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3642747485
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: 9783642747489
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| Contents
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1. Classical Orthogonal Polynomials --; 1.1 An Equation of Hypergeometric Type --; 1.2 Polynomials of Hypergeometric Type and Their Derivatives. The Rodrigues Formula --; 1.3 The Orthogonality Property --; 1.4 The Jacobi, Laguerre, and Hermite Polynomials --; 1.5 Classical Orthogonal Polynomials as Eigenfunctions of Some Eigenvalue Problems --; 2. Classical Orthogonal Polynomials of a Discrete Variable --; 2.1 The Difference Equation of Hypergeometric Type --; 2.2 Finite Difference Analogs of Polynomials of Hypergeometric Type and of Their Derivatives. The Rodrigues Type Formula --; 2.3 The Orthogonality Property --; 2.4 The Hahn, Chebyshev, Meixner, Kravchuk, and Charlier Polynomials --; 2.5 Calculation of Main Characteristics --; 2.6 Asymptotic Properties. Connection with the Jacobi, Laguerre, and Hermite Polynomials --; 2.7 Representation in Terms of Generalized Hypergeometric Functions --; 3. Classical Orthogonal Polynomials of a Discrete Variable on Nonuniform Lattices --; 3.1 The Difference Equation of Hypergeometric Type on a Nonuniform Lattice --; 3.2 The Difference Analogs of Hypergeometric Type Polynomials. The Rodrigues Formula --; 3.3 The Orthogonality Property --; 3.4 Classification of Lattices --; 3.5 Classification of Polynomial Systems on Linear and Quadratic Lattices. The Racah and the Dual Hahn Polynomials --; 3.6 q-Analogs of Polynomials Orthogonal on Linear and Quadratic Lattices --; 3.7 Calculation of the Leading Coefficients and Squared Norms. Tables of Data --; 3.8 Asymptotic Properties of the Racah and Dual Hahn Polynomials --; 3.9 Construction of Some Orthogonal Polynomials on Nonuniform Lattices by Means of the Darboux-Christoffel Formula --; 3.10 Continuous Orthogonality --; 3.11 Representation in Terms of Hypergeometric and q-Hypergeometric Functions --; 3.12 Particular Solutions of the Hypergeometric Type Difference Equation --; Addendum to Chapter 3 --; 4. Classical Orthogonal Polynomials of a Discrete Variable in Applied Mathematics --; 4.1 Quadrature Formulas of Gaussian Type --; 4.2 Compression of Information by Means of the Hahn Polynomials --; 4.3 Spherical Harmonics Orthogonal on a Discrete Set of Points --; 4.4 Some Finite-Difference Methods of Solution of Partial Differential Equations --; 4.5 Systems of Differential Equations with Constant Coefficients. The Genetic Model of Moran and Some Problems of the Queueing Theory --; 4.6 Elementary Applications to Probability Theory --; 4.7 Estimation of the Packaging Capacity of Metric Spaces --; 5. Classical Orthogonal Polynomials of a Discrete Variable and the Representations of the Rotation Group --; 5.1 Generalized Spherical Functions and Their Relations with Jacobi and Kravchuk Polynomials --; 5.2 Clebsch-Gordan Coefficients and Hahn Polynomials --; 5.3 The Wigner 6j-Symbols and the Racah Polynomials --; 5.4 The Wigner 9j-Symbols as Orthogonal Polynomials in Two Discrete Variables --; 5.5 The Classical Orthogonal Polynomials of a Discrete Variable in Some Problems of Group Representation Theory --; 6. Hyperspherical Harmonics --; 6.1 Spherical Coordinates in a Euclidean Space --; 6.2 Solution of the n-Dimensional Laplace Equation in Spherical Coordinates --; 6.3 Transformation of Harmonics Derived in Different Spherical Coordinates --; 6.4 Solution of the Schrödinger Equation for the n-Dimensional Harmonic Oscillator --; Addendum to Chapter 6.
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| Abstract
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While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.
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Mathematical physics.
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Numerical analysis.
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Physics.
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| LC Classification
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QC20.7.O75B937 1991
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| Added Entry
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Arnold F Nikiforov
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Sergei K Suslov
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Vasilii B Uvarov
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