12 of 12 people found the following review helpful
on September 17, 2012
Functions covered are:
Laguerre polynomials, Legendre polynomials, Bessel functions, Chebyshev polynomials, Debye functions, Elliptic function, Error function, Fresnel integrals, Gamma function (Incomplete/Complete), Gegenbauer polynomials, Jacobi polynomials, Hankel functions, Hermite polynomials, Hypergeometric functions, Kelvin's functions, Kummer function, Logarithmic integral, Neumann functions, Riemann Zeta function, Weber-Hermite functions.
The Chapter list is as follows:
1. Series solution of Differential Equations
2. Gamma and Beta functions
3. Legendre polynomials and functions
4. Bessel functions
5. Hermite polynomials
6. Laguerre polynomials
7. Chebyshev polynomials
8. Gegenbauer and Jacobi polynomials
9. Hypergeometric functions
10. Other special functions
All the other functions i listed before are covered in less detail than the main chapter titles. This book has a very great deal of recursive ways of finding identities between special functions and does a good job doing so. I read this to learn more about the special functions i was using in some of my physics classes to get more depth about them and this book definitely covers a good deal of deriving a lot of these interesting identities through mostly recursive relations, summation methods and identities between previously proven functions so there is a lot of flipping if you want to check between steps. I can't say i read this book casually, i actually had to write down some of the equations and work them out myself and it did take a bit of time but i was happy with the result. As for the problems in the book, the proven identities come in very handy when solving some tough problems that would normally take much longer if done using any other methods and are pretty applicable for example some high level physics courses like quantum and statistical mechanics. The book is very cheap for the amount of reference you will get out of it and the added depth on deriving identities for the main chapter equations is really worth it
on April 25, 2015
This is a good text for graduate Engineering students that take a course the incorporates Special Functions in the course material, i.e., Electromagnetics. One can search the Internet for answers on a function like the Gamma Function or you can get this text that contains many of these Special Functions in one place. I found his discussion of the Chebyshev Differential Equation and the resultant solution particularly clear relative to the Chebyshev Polynomial of the 1 st Kind and he removes confusion that is normally in other texts and on-line sources relative to the Chebyshev Polynomial of the 2nd Kind. Bell is very clear in his proofs - they are meant for someone with an applied bent. His material is straightforward and his organization of the material and presentation follow a logical flow. He develops tools and Theorems along the way to achieve an ultimate learning goal for the student. The book is another example where the Senior Editor, John Grafton, and his technical staff at Dover Publications know how to pick classical texts that merit publication.
12 of 18 people found the following review helpful
on October 14, 2007
This book is highly recommended for its clarity; all steps are explained in detail, there are clear examples and the answers to all exercises. The only complaint could be that the independent variable is real and not complex. All books should be written like the author does.