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  • © 2008

Handbook of Continued Fractions for Special Functions

  • A systematic study of continued fraction representations for special functions
  • Verified numerical illustrations of most continued fractions and special functions
  • Only 10% of the continued fractions in this book can be found in the NBS handbook or at the Wolfram website on special functions
  • Special functions are pervasive in all fields of science and industry

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Table of contents (19 chapters)

  1. Front Matter

    Pages I-6
  2. Basic Theory

    1. Front Matter

      Pages 7-7
    2. Basics

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 9-28
    3. Continued fraction representation of functions

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 29-43
    4. Convergence criteria

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 45-58
    5. Padé approximants

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 59-75
    6. Moment theory and orthogonal functions

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 77-104
  3. Numerics

    1. Front Matter

      Pages 105-105
    2. Continued fraction construction

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 107-128
    3. Truncation error bounds

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 129-147
    4. Continued fraction evaluation

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 148-159
  4. Special Functions

    1. Front Matter

      Pages 161-161
    2. On tables and graphs

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 163-173
    3. Mathematical constants

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 175-191
    4. Elementary functions

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 193-220
    5. Gamma function and related functions

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 221-251
    6. Error function and related integrals

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 253-273
    7. Exponential integrals and related functions

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 275-290
    8. Hypergeometric functions

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 291-317
    9. Confluent hypergeometric functions

      • Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
      Pages 319-341

About this book

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies!

But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!

Reviews

From the reviews:

"The book under review is to collect continued fractions for special functions in a friendly volume. … There is no doubt that this book is very useful for the people who need to work with special functions. … The book is suitable for researchers in many fields, so that libraries serving scholars in basic sciences need to have it." (Mehdi Hassani, The Mathematical Association of America, September, 2008)

“The computation of a special function by its development into a continued fraction requires many steps, and that it needs a deep knowledge of theory and practice. The purpose of this handbook is to present the efforts in this direction made by a group of scientists from different universities who have collaborated in the project for many years. … I highly recommend this monograph, a masterpiece, to all those who are interested in continued fractions. It should be on the shelves of every library.” (Claude Brezinski, Journal of Approximation Theory, February, 2010)

Authors and Affiliations

  • Department of Mathematics and Computer Science, University of Antwerp, Belgium

    Annie Cuyt, Brigitte Verdonk

  • Faculty of Teacher and Interpreter Education, Sør-Trøndelag University College, NO-7004 Trondheim, Norway

    Vigdis Brevik Petersen

  • Department of Mathematical Sciences, Norwegian University of Science and Technology, Norway

    Haakon Waadeland

  • Department of Mathematics, University of Colorado, Boulder, USA

    William B. Jones

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access