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Special Functions
Binding: Paperback
Author: George E. Andrews
Manufacturer: Cambridge University Press
Availability: Usually ships in 24 hours
Average Rating: 4.5
Total Customer Reviews: 11
List Price: $63.00
Our Price: $56.70
Sales Rank: 889592
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.
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Users Product Reviews: |
Product Review Summary: Much more advanced than expected This book is more advanced than the description leads you to believe. This is not a book for beginners. Some theorems from real analysis and functional analysis not proved are mentioned by name but not even quoted. Not even the introduction tells the reader that real analysis and functional analysis are needed to understand the book. Besides that, the index is very incomplete. It seems to have been prepared by randomly picking pages.
Product Review Summary: A disappointment I ordered this book through the mail and as soon as I opened it it was a disappointment. The paper quality is average, the typesetting bland and the formulas unappealing, and most importantly, the information incomplete and poorly structured.
I had especially been hoping for good coverage of orthogonal polynomials but especially their presentation in this book is very weak: the historical perspective is entirely lacking as is the common theory underlying the classical orthogonal polynomials, and the generating functions which play a crucial role are not even mentioned.
In general the book pays no attention to numerical methods for the evaluation of the functions.
The scant material on the Gamma and Zeta function shows little insight. There is no mention of the role of the Euler-MacLaurin summation formula to obtain amongst other Stirling's formula for the Gamma Function.
The book is structured as are many mathematics books nowadays: Lemma ... Proof etcetera, which is exactly how mathematics books should not be written, in my opinion of course.
As a matter of comparison look at H.M. Edwards's lovely book "Riemann's Zeta Function" which has nice little chapters, each with an explanatory header, where the material is put in historical context, any difficulties are outlined, and the importance of the result is evaluated.
Finally, since this book is part of a series supposed to be some kind of a Mathematics Encyclopedia, I seriously wonder what the purpose is of the exercises or even the proofs.
Instead of this hodge-podge of results, one could get for less than half the price the beautiful and insightful book by Hochstadt (The Functions of Mathematical Physics) which covers Orthogonal Polynomials and the Hypergeometric and Confluent Hypergeometric Functions and also Bessel Functions and more... PLUS [Richard R. Silverman's translation of] N.N. Lebedev (Special Functions & their Applications), which has several chapters on Orthogonal Polynomials.
Product Review Summary: A Modern Whittaker and Watson, Buy It 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.
Product Review Summary: A book comes close to " A course of modern analysis " 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.
Product Review Summary: clean and concise 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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