Orthogonal Polynomials of Several Variables.
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| Author / Creator: | Dunkl, Charles F. |
|---|---|
| Edition: | 2nd ed. |
| Imprint: | Cambridge : Cambridge University Press, 2014. |
| Description: | 1 online resource (440 pages) |
| Language: | English |
| Series: | Encyclopedia of Mathematics and its Applications ; v. 155 Encyclopedia of mathematics and its applications. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/12015594 |
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| 100 | 1 | |a Dunkl, Charles F. | |
| 245 | 1 | 0 | |a Orthogonal Polynomials of Several Variables. |
| 250 | |a 2nd ed. | ||
| 260 | |a Cambridge : |b Cambridge University Press, |c 2014. | ||
| 300 | |a 1 online resource (440 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. 155 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Half-Title page; Series page; Title page; Copyright page; Dedication page; Contents; Preface to the Second Edition; Preface to the First Edition; 1 Background; 1.1 The Gamma and Beta Functions; 1.2 Hypergeometric Series; 1.2.1 Lauricella 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. | |
| 505 | 8 | |a 1.5.2 Generalized Gegenbauer polynomials1.5.3 A limiting relation; 1.6 Notes; 2 Orthogonal Polynomials in Two Variables; 2.1 Introduction; 2.2 Product Orthogonal Polynomials; 2.3 Orthogonal Polynomials on the Unit Disk; 2.4 Orthogonal Polynomials on the Triangle; 2.5 Orthogonal Polynomials and Differential Equations; 2.6 Generating Orthogonal Polynomials of Two Variables; 2.6.1 A method for generating orthogonal polynomials; 2.6.2 Orthogonal polynomials for a radial weight; 2.6.3 Orthogonal polynomials in complex variables; 2.7 First Family of Koornwinder Polynomials. | |
| 505 | 8 | |a 2.8 A Related Family of Orthogonal Polynomials2.9 Second Family of Koornwinder Polynomials; 2.10 Notes; 3 General Properties of Orthogonal Polynomials in Several Variables; 3.1 Notation and Preliminaries; 3.2 Moment Functionals and Orthogonal Polynomials in Several Variables; 3.2.1 Definition of orthogonal polynomials; 3.2.2 Orthogonal polynomials and moment matrices; 3.2.3 The moment problem; 3.3 The Three-Term Relation; 3.3.1 Definition and basic properties; 3.3.2 Favard''s theorem; 3.3.3 Centrally symmetric integrals; 3.3.4 Examples; 3.4 Jacobi Matrices and Commuting Operators. | |
| 505 | 8 | |a 3.5 Further Properties of the Three-Term Relation3.5.1 Recurrence formula; 3.5.2 General solutions of the three-term relation; 3.6 Reproducing Kernels and Fourier Orthogonal Series; 3.6.1 Reproducing kernels; 3.6.2 Fourier orthogonal series; 3.7 Common Zeros of Orthogonal Polynomials in Several Variables; 3.8 Gaussian Cubature Formulae; 3.9 Notes; 4 Orthogonal Polynomials on the Unit Sphere; 4.1 Spherical Harmonics; 4.2 Orthogonal Structures on S[sup(d)] and on B[sup(d)]; 4.3 Orthogonal Structures on B[sup(d)] and on S[sup(d+m-1)]; 4.4 Orthogonal Structures on the Simplex. | |
| 505 | 8 | |a 4.5 Van der Corput -- Schaake Inequality4.6 Notes; 5 Examples of Orthogonal Polynomials in Several Variables; 5.1 Orthogonal Polynomials for Simple Weight Functions; 5.1.1 Product weight functions; 5.1.2 Rotation-invariant weight functions; 5.1.3 Multiple Hermite polynomials on R[sup(d)]; 5.1.4 Multiple Laguerre polynomials on R[sub(+)sup(d)]; 5.2 Classical Orthogonal Polynomials on the Unit Ball; 5.2.1 Orthonormal bases; 5.2.2 Appell''s monic orthogonal and biorthogonalpolynomials; 5.2.3 Reproducing kernel with respect to W[sup(B) sub[Mu] on B[sup(d)]. | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 520 | |a Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade. | ||
| 650 | 0 | |a Orthogonal polynomials. |0 http://id.loc.gov/authorities/subjects/sh85095794 | |
| 650 | 0 | |a Functions of several real variables. |0 http://id.loc.gov/authorities/subjects/sh85052359 | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Functions of several real variables. |2 fast |0 (OCoLC)fst00936124 | |
| 650 | 7 | |a Orthogonal polynomials. |2 fast |0 (OCoLC)fst01048521 | |
| 650 | 1 | 7 | |a Orthogonale reeksen. |2 gtt |0 (NL-LeOCL)07861760X |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Xu, Yuan. | |
| 776 | 0 | 8 | |i Print version: |a Dunkl, Charles F. |t Orthogonal Polynomials of Several Variables. |d Cambridge : Cambridge University Press, ©2014 |z 9781107071896 |
| 830 | 0 | |a Encyclopedia of mathematics and its applications. |0 http://id.loc.gov/authorities/names/n42010632 | |
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| 928 | |t Library of Congress classification |a QA404.5 .D86 2014 |l Online |c UC-FullText |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=805504 |z eBooks on EBSCOhost |g ebooks |i 12414664 | ||