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Beschreibung
The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painlevé transcendents, which have been termed the 'special functions of the twenty-first century'.
The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painlevé transcendents, which have been termed the 'special functions of the twenty-first century'.
Über den Autor
Richard Beals is a former Professor of Mathematics at the University of Chicago and Yale University. He is the author or co-author of books on mathematical analysis, linear operators and inverse scattering theory, and has authored more than 100 research papers in areas including partial differential equations, mathematical economics and mathematical psychology.
Inhaltsverzeichnis
1. Orientation; 2. Gamma, beta, zeta; 3. Second-order differential equations; 4. Orthogonal polynomials on an interval; 5. The classical orthogonal polynomials; 6. Semiclassical orthogonal polynomials; 7. Asymptotics of orthogonal polynomials: two methods; 8. Confluent hypergeometric functions; 9. Cylinder functions; 10. Hypergeometric functions; 11. Spherical functions; 12. Generalized hypergeometric functions; G-functions; 13. Asymptotics; 14. Elliptic functions; 15. Painlevé transcendents; Appendix A. Complex analysis; Appendix B. Fourier analysis; References; Index.
Details
Erscheinungsjahr: 2016
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
ISBN-13: 9781107106987
ISBN-10: 1107106982
Sprache: Englisch
Einband: Gebunden
Autor: Beals, Richard
Wong, Roderick
Hersteller: Cambridge University Press
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 235 x 157 x 33 mm
Von/Mit: Richard Beals (u. a.)
Erscheinungsdatum: 28.11.2016
Gewicht: 0,936 kg
Artikel-ID: 114441835

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