Special Functions by George E Andrews

Special Functions by George E Andrews

Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This clearly expressed and readable work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics.

'Occasionally there is published a mathematics book that one is compelled to describe as, well, let us say, specialSpecial Functions is certainly one of those rare books. … this treatise … should become a classic. Every student, user, and researcher in analysis will want to have it close at hand as she/he works.' The Mathematical Intelligencer
' … the material is written in an excellent manner … I recommend this book warmly as a rich source of information to everybody who is interested in 'Special Functions'.' Zentralblatt MATH
' … this book contains a wealth of fascinating material which is presented in a user-friendly way. If you want to extend your knowledge of special functions, this is a good place to start. Even if your interests are in number theory or combinatorics, there is something for you too … the book can be warmly recommended and should be in all good libraries.' Adam McBride, The Mathematical Gazette
' … it comes into the range of affordable books that you want to (and probably should have on your desk'. Jean Mawhin, Bulletin of the Belgian Mathematical Society
'The book is full of beautiful and interesting formulae, as was always the case with mathematics centred around special functions. It is written in the spirit of the old masters, with mathemtics developed in terms of formulas. There are many historical comments in the book. It can be recommended as a very useful reference.' European Mathematical Society
'… full of beautiful and interesting formulae … It can be recommended as a very useful reference.' EMS Newsletter
'a very erudite text and reference in special functions' Allen Stenger, MAA Reviews

Roy, Ranjan: - Ranjan Roy (1947-2020) was the Ralph C. Huffer Professor of Mathematics and Astronomy at Beloit College, where he was a faculty member for 38 years. Roy published papers and reviews on Riemann surfaces, differential equations, fluid mechanics, Kleinian groups, and the development of mathematics. He was an award-winning educator, having received the Allendoerfer Prize, the Wisconsin MAA teaching award, and the MAA Haimo Award for Distinguished Mathematics Teaching and was twice named Teacher of the Year at Beloit College. He coauthored Special Functions (2001) with George Andrews and Richard Askey and coauthored chapters in the NIST Handbook of Mathematical Functions (2010); he also authored Elliptic and Modular Functions from Gauss to Dedekind to Hecke (2017) and the first edition of this book, Sources in the Development of Mathematics (2011).

SKU	Unavailable
ISBN 13	9780521789882
ISBN 10	0521789885
Title	Special Functions
Author	George E Andrews
Series	Encyclopedia Of Mathematics And Its Applications
Condition	Unavailable
Binding Type	Paperback
Publisher	Cambridge University Press
Year published	2001-01-29
Number of pages	682
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.