Special Functions: A Graduate Text

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August 2010



The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.


Preface; 1. Orientation; 2. Gamma, beta, zeta; 3. Second order differential equations; 4. Orthogonal polynomials; 5. Discrete orthogonal polynomials; 6. Confluent hypergeometric functions; 7. Cylinder functions; 8. Hypergeometric functions; 9. Spherical functions; 10. Asymptotics; 11. Elliptic functions; References; Index.


Richard Beals is Professor Emeritus of Mathematics at Yale University. Roderick Wong is Professor of Mathematics and Vice President for Research at the City University of Hong Kong.


'One of the most remarkable facts of this book is its goal to be useful for self-study ... highly recommended textbook.' Mathematical Reviews 'Although there have been many monographs on special functions since Whittaker and Watson ['s A Course of Modern Analysis, 4th edition] we can anticipate that Beals and Wong will become a classic textbook for graduate students in math, applied math, and physics. Don't delay in becoming familiar with it!' SIAM Review
EAN: 9780521197977
ISBN: 052119797X
Untertitel: 'Cambridge Studies in Advanced'. Sprache: Englisch.
Erscheinungsdatum: August 2010
Seitenanzahl: 456 Seiten
Format: gebunden
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