Abstract
The revived interest in continued fractions stems from the fact that many special functions enjoy easy to handle and rapidly converging continued fraction representations. These can be made to good use in a project that envisages the provably correct (or interval) evaluation of these functions. Of course, first a catalogue of these continued fraction representations needs to be put together.
The Handbook of continued fractions for special functions is the result of a systematic study of series and continued fraction representations for several families of mathematical functions used in science and engineering. Only 10% of the listed continued fraction representations can also be found in the famous NBS Handbook edited by Abramowitz and Stegun. More information is given in Sect. 1.
The new handbook is brought to life at the website www.cfhblive.ua.ac.be where visitors can recreate tables to their own specifications, and can explore the numerical behaviour of the series and continued fraction representations. An easy web interface supporting these features is discussed in the Sects. 2, 3 and 4.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz, M., Stegun, I.: Handbook of mathematical functions with formulas, graphs and mathematical tables. U.S. Government Printing Office, NBS, Washington, D. C (1964)
Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.: Higher transcendental functions, vol. 1. McGraw-Hill, New York (1953)
Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.: Higher transcendental functions, vol. 2. McGraw-Hill, New York (1953)
Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.: Higher transcendental functions, vol. 3. McGraw-Hill, New York (1955)
Cipra, B.A.: A new testament for special functions? SIAM News 31(2) (1998)
Lozier, D.: NIST Digital Library of Mathematical Functions. Annals of Mathematics and Artificial Intelligence 38(1–3) (May 2003)
Moler, C.: The tetragamma function and numerical craftmanship. MATLAB News & Notes (2002)
Cuyt, A., Brevik Petersen, V., Verdonk, B., Waadeland, H., Jones, W.B.: Handbook of Continued Fractions for Special Functions. Springer, Heidelberg (2008)
Backeljauw, F., Cuyt, A.: A continued fraction package for special functions. ACM Transactions on Mathematical Software (submitted, 2008)
Backeljauw, F., Becuwe, S., Cuyt, A.: Validated evaluation of special mathematical functions. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.) AISC 2008, Calculemus 2008, and MKM 2008. LNCS (LNAI), vol. 5144, pp. 206–216. Springer, Heidelberg (2008)
Floating-Point Working Group: IEEE standard for binary floating-point arithmetic. SIGPLAN 22, 9–25 (1987)
Muller, J.-M.: Elementary functions: Algorithms and implementation. Birkhäuser, Basel (1997)
Cuyt, A., Verdonk, B., Waadeland, H.: Efficient and reliable multiprecision implementation of elementary and special functions. SIAM J. Sci. Comput. 28(4), 1437–1462 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cuyt, A., Backeljauw, F., Becuwe, S., Colman, M., Docx, T., Van Deun, J. (2009). Continued Fractions for Special Functions: Handbook and Software. In: Cuyt, A., Krämer, W., Luther, W., Markstein, P. (eds) Numerical Validation in Current Hardware Architectures. Lecture Notes in Computer Science, vol 5492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01591-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-01591-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01590-8
Online ISBN: 978-3-642-01591-5
eBook Packages: Computer ScienceComputer Science (R0)