PDF Ebook Special Functions (Encyclopedia of Mathematics and its Applications), by George E. Andrews, Richard Askey, Ranjan Roy
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Special Functions (Encyclopedia of Mathematics and its Applications), by George E. Andrews, Richard Askey, Ranjan Roy
PDF Ebook Special Functions (Encyclopedia of Mathematics and its Applications), by George E. Andrews, Richard Askey, Ranjan Roy
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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.
- Sales Rank: #3222292 in Books
- Brand: Brand: Cambridge University Press
- Published on: 1999-01-13
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.46" w x 6.14" l, 2.49 pounds
- Binding: Hardcover
- 684 pages
- Used Book in Good Condition
Review
"...the authors demonstrate a superb familiarity with the historical roots of their subject...All of the chapters are beautifully written...wonderful historical insights...Special Functions will certainly emerge as the chief textbook and reference on special functions for the next several years...This book joins F. W. J. Olver's Asymptotics and Special Functions, first published in 1974 [Academic Press, New York; MR 55 #8655], as the only general books on special functions during the past three decades that belong 'in the Hobbs class,' to quote G. H. Hardy." Mathematical Reviews
"The book is packed with brief, challenging superveniences that make it a browser's delight. One of the delightful features of this book is how the sense of history, of mathematics being created and savored, informs the text. This is a splendid work, and I predict that it will be a bestseller as well." Bulletin of the American Mathematical Society
Most helpful customer reviews
0 of 0 people found the following review helpful.
Five Stars
By Ronnie
A good dictionary for the researcher, not proper for the beginners.
5 of 9 people found the following review helpful.
A book comes close to " A course of modern analysis "
By Wan Koon Yat
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.
30 of 30 people found the following review helpful.
Encyclopedic and highly readable book on Special Functions
By A Customer
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.
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