UID:
almahu_9949199487702882
Umfang:
XVI, 374 p.
,
online resource.
Ausgabe:
1st ed. 1991.
ISBN:
9783642747489
Serie:
Scientific Computation,
Anmerkung:
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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783642747502
Weitere Ausg.:
Printed edition: ISBN 9783540511236
Weitere Ausg.:
Printed edition: ISBN 9783642747496
Sprache:
Englisch
DOI:
10.1007/978-3-642-74748-9
URL:
https://doi.org/10.1007/978-3-642-74748-9
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