Skip to content
Register Sign in Wishlist
Special Functions

Special Functions


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 2001
  • availability: Available
  • format: Paperback
  • isbn: 9780521789882

£ 59.99

Add to cart Add to wishlist

Other available formats:
Hardback, eBook

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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.

    • Authors are world experts in this subject
    • Broad applicability throughout mathematics and physics
    • Emphasis on computational formulas
    Read more

    Reviews & endorsements

    'Occasionally there is published a mathematics book that one is compelled to describe as, well, let us say, special. Special 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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: April 2001
    • format: Paperback
    • isbn: 9780521789882
    • length: 682 pages
    • dimensions: 235 x 161 x 36 mm
    • weight: 0.96kg
    • availability: Available
  • Table of Contents

    1. The Gamma and Beta functions
    2. The hypergeometric functions
    3. Hypergeometric transformations and identities
    4. Bessel functions and confluent hypergeometric functions
    5. Orthogonal polynomials
    6. Special orthogonal transformations
    7. Topics in orthogonal polynomials
    8. The Selberg integral and its applications
    9. Spherical harmonics
    10. Introduction to q-series
    11. Partitions
    12. Bailey chains
    Appendix 1. Infinite products
    Appendix 2. Summability and fractional integration
    Appendix 3. Asymptotic expansions
    Appendix 4. Euler-Maclaurin summation formula
    Appendix 5. Lagrange inversion formula
    Appendix 6. Series solutions of differential equations.

  • Authors

    George E. Andrews, Pennsylvania State University

    Richard Askey, University of Wisconsin, Madison

    Ranjan Roy, Beloit College, Wisconsin

Related Books

also by this author

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.