Special Functions | 
 enlarge | Authors: George E. Andrews, Richard Askey, Ranjan Roy
Publisher: Cambridge University Press
Category: Book
List Price: $62.00
Buy New: $52.12
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Rating:  10 reviews
Sales Rank: 631167
Media: Paperback
Edition: 1
Pages: 620
Number Of Items: 1
Shipping Weight (lbs): 2
Dimensions (in): 9.1 x 6.1 x 1.5
ISBN: 0521789885
Dewey Decimal Number: 512
EAN: 9780521789882
Publication Date: February 15, 2001
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Condition: Brand new item. Over 4 million customers served. Order now. Selling online since 1995. Few left in stock - order soon. Code: C20081118203843B
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Product Description
Special functions, which include the trigonometric functions, have been used for centuries. Their role in the solution of differential equations was exploited by Newton and Leibniz, and the subject of special functions has been in continuous development ever since. In just the past thirty years several new special functions and applications have been discovered. This treatise presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series. It includes both important historical results and recent developments and shows how these arise from several areas of mathematics and mathematical physics. Particular emphasis is placed on formulas that can be used in computation. The book begins with a thorough treatment of the gamma and beta functions that are essential to understanding hypergeometric functions. Later chapters discuss Bessel functions, orthogonal polynomials and transformations, the Selberg integral and its applications, spherical harmonics, q-series, partitions, and Bailey chains. This clear, authoritative work will be a lasting reference for students and researchers in number theory, algebra, combinatorics, differential equations, applied mathematics, mathematical computing, and mathematical physics.
Book Description
Special functions, which include the trigonometric functions, have been used for centuries. Their role in the solution of differential equations was exploited by Newton and Leibniz, and the subject of special functions has been in continuous development ever since. This treatise presents an overview of the area of special functions, focusing on the hypergeometric functions and the associated hypergeometric series. It includes both important historical results and recent developments and shows how these arise from several areas of mathematics and mathematical physics. Particular emphasis is placed on formulas that can be used in computation.This clear, authoritative work will be a lasting reference for students and researchers in number theory, algebra, combinatorics, differential equations, mathematical computing, and mathematical physics.
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| Customer Reviews: Read 5 more reviews...
 Encyclopedic and highly readable book on Special Functions June 7, 1999
27 out of 27 found this review helpful
This is one of the best books on Mathematics I have read recently;reading it gave me pleasure similar to I had felt while reading classics such as Hardy's Pure Mathematics and Titchmarsh's Theory of Functions about 30 years ago. Starting with a thorough and encyclopedic treatment of Gamma Functions , the book develops, rightly, the thesis of grandeur and ubiquitousness of Hypergeometric Functions,to then cover some of the most important special functions known today. And the beauty lies in precise,to the point, yet historically complete and 'multi-angled' as well as rigourous treatment of every topic covered, with a large number of exercises of nontrivial nature dealing successfully with details which probably could not be included in the main text because of desire to keep the size of the book within reasonable limits. Nonetheless, the authors have delightfully and almost magically been able to cover a lot of ground in a mere 600 odd pages.
A Modern Whittaker and Watson, Buy It October 24, 2004
MathGeek741 (Maryland, USA)
4 out of 4 found this review helpful
This book is great. It is the best overview I have ever seen of the primary special functions, as seen from a modern viewpoint. Buy it and you will spend many happy hours reading the theorems it contains, and doing the excercizes at the end of each chapter.
Encyclopedic and highly readable book on Special Functions June 7, 1999
2 out of 2 found this review helpful
This is one of the best books on Mathematics I have read recently;reading it gave me pleasure similar to I had felt while reading classics such as Hardy's Pure Mathematics and Titchmarsh's Theory of Functions about 30 years ago. Starting with a thorough and encyclopedic treatment of Gamma Functions , the book develops, rightly, the thesis of grandeur and ubiquitousness of Hypergeometric Functions,to then cover some of the most important special functions known today. And the beauty lies in precise,to the point, yet historically complete and 'multi-angled' as well as rigourous treatment of every topic covered, with a large number of exercises of nontrivial nature dealing successfully with details which probably could not be included in the main text because of desire to keep the size of the book within reasonable limits. Nonetheless, the authors have delightfully and almost magically been able to cover a lot of ground in a mere 600 odd pages.
A book comes close to " A course of modern analysis " August 7, 2001
Wan Koon Yat (North Point Hong Kong)
5 out of 8 found this review helpful
Though this book cannot be compared to Whittaker and Watson's classic book. It comes quite close to it. I just want to comment on the the area covers are too concentrated and the rigorous manner which is the hall mark of " Modern Analysis " is lacking. Anyway, this book deserves 5 stars.
clean and concise February 11, 2001
roy ho (toronto, ontario)
3 out of 5 found this review helpful
It has a very good style of writing for the nature of mathematics. It is clean, no unnecessary explanation or examples. In a way, one can feel something similar to Axler's. It is an excellent reference book. One should keep this book just as Axler's Linear Algebra Done Right, Numerical Recipe, DE Knuth's Art of Programming.
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