Continued Fractions for Special Functions: Handbook and Software

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 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.