Authors:
- 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)
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Front Matter
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Numerics
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Front Matter
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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
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Department of Mathematics and Computer Science, University of Antwerp, Belgium
Annie Cuyt, Brigitte Verdonk
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Faculty of Teacher and Interpreter Education, Sør-Trøndelag University College, NO-7004 Trondheim, Norway
Vigdis Brevik Petersen
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Department of Mathematical Sciences, Norwegian University of Science and Technology, Norway
Haakon Waadeland
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Department of Mathematics, University of Colorado, Boulder, USA
William B. Jones
Bibliographic Information
Book Title: Handbook of Continued Fractions for Special Functions
Authors: Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, William B. Jones
DOI: https://doi.org/10.1007/978-1-4020-6949-9
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2008
Hardcover ISBN: 978-1-4020-6948-2Published: 22 April 2008
Softcover ISBN: 978-90-481-7775-2Published: 19 October 2010
eBook ISBN: 978-1-4020-6949-9Published: 12 April 2008
Edition Number: 1
Number of Pages: XVI, 431
Topics: Special Functions, Mathematical and Computational Engineering, Mathematics, general, Mathematics of Computing, Engineering, general, Science, Humanities and Social Sciences, multidisciplinary