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Classical and Quantum Orthogonal Polynomials in One Variable.
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2005.
|
| Colección: | Encyclopedia of mathematics and its applications.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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|---|---|---|---|
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| 003 | OCoLC | ||
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| 100 | 1 | |a Ismail, Mourad E. H. | |
| 245 | 1 | 0 | |a Classical and Quantum Orthogonal Polynomials in One Variable. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2005. | ||
| 300 | |a 1 online resource (728 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of Mathematics and its Applications ; |v v. 98 | |
| 505 | 0 | |a Cover; Half Title; Series Page; Title; Copyright; Contents; Foreword; Preface; 1 Preliminaries; 1.1 Hermitian Matrices and Quadratic Forms; 1.2 Some Real and Complex Analysis; 1.3 Some Special Functions; 1.4 Summation Theorems and Transformations; Exercises; 2 Orthogonal Polynomials; 2.1 Construction of Orthogonal Polynomials; 2.2 Recurrence Relations; 2.3 Numerator Polynomials; 2.4 Quadrature Formulas; 2.5 The Spectral Theorem; 2.6 Continued Fractions; 2.7 Modifications of Measures: Christoffel and Uvarov; 2.8 Modifications of Measures: Toda; 2.9 Modification by Adding Finite Discrete Parts. | |
| 505 | 8 | |a 2.10 Modifications of Recursion Coefficients2.11 Dual Systems; Exercises; 3 Differential Equations Discriminants and Electrostatics; 3.1 Preliminaries; 3.2 Differential Equations; 3.3 Applications; 3.4 Discriminants; 3.5 An Electrostatic Equilibrium Problem; 3.6 Functions of the Second Kind; 3.7 Differential Relations and Lie Algebras; Exercises; 4 Jacobi Polynomials; 4.1 Orthogonality; 4.2 Differential and Recursion Formulas; 4.3 Generating Functions; 4.4 Functions of the Second Kind; 4.5 Ultraspherical Polynomials; 4.6 Laguerre and Hermite Polynomials; 4.7 Multilinear Generating Functions. | |
| 505 | 8 | |a 4.8 Asymptotics and Expansions4.9 Relative Extrema of Classical Polynomials; 4.10 The Bessel Polynomials; Exercises; 5 Some Inverse Problems; 5.1 Ultraspherical Polynomials; 5.2 Birth and Death Processes; 5.3 The Hadamard Integral; 5.4 Pollaczek Polynomials; 5.5 A Generalization; 5.6 Associated Laguerre and Hermite Polynomials; 5.7 Associated Jacobi Polynomials; 5.8 The J-Matrix Method; 5.9 The Meixner-Pollaczek Polynomials; Exercises; 6 Discrete Orthogonal Polynomials; 6.1 Meixner Polynomials; 6.2 Hahn, Dual Hahn, and Krawtchouk Polynomials; 6.3 Difference Equations. | |
| 505 | 8 | |a 6.4 Discrete Discriminants6.5 Lommel Polynomials; 6.6 An Inverse Operator; Exercises; 7 Zeros and Inequalities; 7.1 A Theorem of Markov; 7.2 Chain Sequences; 7.3 The Hellmann-Feynman Theorem; 7.4 Extreme Zeros of Orthogonal Polynomials; 7.5 Concluding Remarks; 8 Polynomials Orthogonal on the Unit Circle; 8.1 Elementary Properties; 8.2 Recurrence Relations; 8.3 Differential Equations; 8.4 Functional Equations and Zeros; 8.5 Limit Theorems; 8.6 Modifications of Measures; Exercises; 9 Linearization, Connections and Integral Representations; 9.1 Connection Coefficients. | |
| 505 | 8 | |a 9.2 The Ultraspherical Polynomials and Watson's Theorem9.3 Linearization and Power Series Coefficients; 9.4 Linearization of Products and Enumeration; 9.5 Representations for Jacobi Polynomials; 9.6 Addition and Product Formulas; 9.7 The Askey-Gasper Inequality; Exercises; 10 The Sheffer Classification; 10.1 Preliminaries; 10.2 Delta Operators; 10.3 Algebraic Theory; Exercises; 11 q-Series Preliminaries; 11.1 Introduction; 11.2 Orthogonal Polynomials; 11.3 The Bootstrap Method; 11.4 q-Differences; 12 q-Summation Theorems; 12.1 Basic Definitions; 12.2 Expansion Theorems; 12.3 Bilateral Series. | |
| 500 | |a 12.4 Transformations. | ||
| 520 | |a The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Orthogonal polynomials. | |
| 650 | 6 | |a Polynômes orthogonaux. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Orthogonal polynomials |2 fast | |
| 650 | 7 | |a Orthogonale Polynome |2 gnd | |
| 650 | 1 | 7 | |a Orthogonale reeksen. |2 gtt |
| 776 | 0 | 8 | |i Print version: |a Ismail, Mourad E.H. |t Classical and Quantum Orthogonal Polynomials in One Variable. |d Cambridge : Cambridge University Press, ©2005 |z 9780521782012 |
| 830 | 0 | |a Encyclopedia of mathematics and its applications. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569255 |z Texto completo |
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