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OverviewThe 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'. Full Product DetailsAuthor: Richard Beals (Yale University, Connecticut) , Roderick Wong (City University of Hong Kong)Publisher: Cambridge University Press Imprint: Cambridge University Press Edition: 2nd Revised edition Volume: 153 Dimensions: Width: 15.40cm , Height: 3.20cm , Length: 23.70cm Weight: 0.780kg ISBN: 9781107106987ISBN 10: 1107106982 Pages: 488 Publication Date: 17 May 2016 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1. 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.Reviews'... an excellent graduate textbook, one of the two best available on this subject...' Warren Johnson, MAA Reviews (www.maa.org) Author InformationRichard 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. Roderick Wong is Chair Professor of Mathematics at the City University of Hong Kong. He is the author of books on asymptotic approximations of integrals and applied analysis. He has published over 140 research papers in areas such as asymptotic analysis, singular perturbation theory and special functions. Tab Content 6Author Website:Countries AvailableAll regions |
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