Special Functions [Paperback]

Z. X. Wang (Author), D. R. Guo (Author)

Book Description

Publication Date: December 1988 | ISBN-10: 997150667X | ISBN-13: 978-9971506674

In this book, expansions of functions in infinite series and infinite product and the asymptotic expansion of functions are discussed. This may be the best reference book on Special Functions.

--This text refers to an out of print or unavailable edition of this title.

Editorial Reviews

Review

"In January 1980 when I visited Beijing, Professor Z X Wang, my MSc thesis advisor of many years ago, gave me a copy of his book with Mr D R Guo on Special Functions. On many occasions in the later years, I had consulted the book for various things such as the hypergeometric series and the elliptic functions. The book is systematic, clear and to the point, as one would expect from Professor Wang's style and personality. It is great news that the book is now being published in an English translation. It will benefit many students and research workers who do not read Chinese." Foreword from C N Yang" Nobel Laureate "This is quite a comprehensive treatise on special functions ... This book should very well serve as a reference book for the topics listed above." Monatshefte fur Mathematik, 1991 "The book is a welcome addition to the classical works on special functions. The presentation is very clear. The great variety of topics makes it a useful and instructive source of information for many workers in physics, engineering and applied mathematics." Mathematics Abstracts

Product Details

• Paperback: 720 pages
• Publisher: World Scientific Pub Co Inc (December 1988)
• Language: English
• ISBN-10: 997150667X
• ISBN-13: 978-9971506674
• Product Dimensions: 8.3 x 5.9 x 1.4 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,010,693 in Books (See Top 100 in Books)

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11 of 11 people found the following review helpful:

5.0 out of 5 stars Great complement to Whittaker and Watson., January 15, 2006

By 

solar-bear - See all my reviews

This review is from: Special Functions (Paperback)

This is an outstanding book on special functions though it doesn't seem well known in the West. At first sight it appears to follow the path of Whittaker and Watson, but on closer examination it actually treats the subject(s) quite differently, sometimes better, dare I say. Among its strengths are (a) all derivations are carried out in detail; (b) the author takes great care to motivate various techniques so that they seem perfectly natural; (c) the contour-integral method is used extensively to solve the differential equations associated with the special functions; and (d) the infinite-series approach to solving the differential equations, which Whittaker and Watson develops theoretically but does not apply, is carried out more thoroughly here than anywhere else.

Point (b) should greatly appeal to the physics type, and it came somewhat as a surprise to me, since I had the impression that most Chinese professors had a very condensed writing style, in which motivation isn't the top priority. On the other hand, the contour-integral-solution approach to ODEs is basically absent (at least not systematically employed) in Whittaker and Watson. When you look at the integral representations of the special functions in the book, there is less of the feeling that they just dropped out of the sky. Point (d) should appeal tremendously to most of the readers, since a typical physics/mathematics student learns the series technique in his/her second course on ODE. The coverage here is outstanding because the author does not summarily dispatch, as most others do, treatment of the irregular solutions, ie, the "bad-boy" solutions which arise when the difference of the roots of the indicial equation equals zero or an integer. Whittaker and Watson, for example, relegates the subject to a footnote in their treatment of the hypergeometric function.

The original author (Wang) wrote the book in Chinese, which was translated into English by two of his students. You can easily tell even without seeing the author list that two translators were involved. One has a better command of English and his prose is more fluid.

Of course, for a subject as classical as special functions, there is bound to be a great deal of overlap between any two books in terms of the topics covered. Without a doubt Whittaker and Watson is still King in this area, but at least for me this book is Queen. Highly recommended.

7 of 9 people found the following review helpful:

5.0 out of 5 stars A classic, only Mordern Analysis can upstage it., February 3, 2003

By 

Wan Koon Yat "wankoonyat" (North Point Hong Kong) - See all my reviews
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Amazon Verified Purchase

This review is from: Special Functions (Paperback)

Prof Wang ' Specal fuctions is a classic on specai functions,
In fact Prof, Wang was also an admirer of Modern Analysis.
The style of writting this book is in fact follows the style
of Modern Analysis, That is why is so good. But of course
Prof Wang had his own scheme and add topics not included
in Modern Analysis. To me, the best part is on the elliptic integrals and elliptic functions. I cannot find another book
on this subject which is started with basic theories, then
step by step, to introduce you to more advanced theories
from more simple theories.
Moreover, this book is originally written in Chinese.
Now it is tranalated in English.
This quality of this book is camparable to other famous books
on special functions like George Adrewo's or J. W. L. Olver's.
As a Chinese, I am proud of that and also give my repsect to
Prof Wang, whose contribution to Scientic developmeant in
China cannot over overestimated!