Customer Reviews

Special Functions (Encyclopedia of Mathematics and its Applications)

5 star:		(10)
4 star:		(0)
3 star:		(0)
2 star:		(1)
1 star:		(1)

 

 

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.

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.

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.

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.

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.

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.

Professor Roy et al have made Special Functions clearer to me in this comprehensive volume than any previous authors I have read.

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.

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.

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.