| The study of orthogonal polynomials of several variables goes back at least as far as Hermite. There have been only a few books on the subject since: Appell and de Feriet [1926] and Erdelyi et al. [1953]. Twenty-five years have gone by since Koornwinder's survey article [1975]. A number of individuals who need techniques from this topic have approached us and suggested (even asked) that we write a book accessible to a general mathematical audience. It is our goal to present the developments of very recent research to a readership trained in classical analysis. We include applied mathematicians and physicists, and even chemists and mathematical biologists, in this category. 本书为英文版。 |
| Preface 1 Background 1.1 The Gamma and Beta Functions 1.2 Hypergeometric Series 1.3 Orthogonal Polynomials of One Variable 1.3.1 General properties 1.3.2 Three term recurrence 1.4 Classical Orthogonal Polynomials 1.4.1 Hermite polynomials 1.4.2 Laguerre polynomials 1.4.3 Gegenbauer polynomials 1.4.4 Jacobi polynomials 1.5 Modified Classical Polynomials 1.5.1 Generalized Hermite polynomials 1.5.2 Generalized Gegenbauer. polynomials 1.5.3 A limiting relation 1.6 Notes 2 Examples of Orthogonal Polynomials in Several Variables 2.1 Notation and Preliminary 2.2 Spherical Harmonics 2.3 Classical Orthogonal Polynomials 2.3.1 Multiple Jacobi polynomials on the cube 2.3.2 Classical orthogonal polynomals on the unit ball 2.3.3 Classical orthogonal polynomials on the simples 2.3.4 Multiple Hermite polynomials on Rd 2.3.5 Multiple Laguerre polynomials on Rd+ …… 3 General Properties of Orthogonal Polynomials in Several Variables 4 Root Systems and Coxeter guoups 5 Spherical Harmonics Associated With Reflection Guoups 6 Classical and Generalized Classical Orthogonal Polynomials 7 Summability of Orthogonal Expansions 8 Orthogonal Polynomials Associated with Symmetric Groups 9 Orthogoanl Polynomials Associated with Octahedral Guoups and Applications Bibliography Author index Symbol index Subject index |
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