Unrestricted algorithms for elementary and special functions

Details Unrestricted algorithms for elementary and special functions Unrestricted algorithms for elementary and special functions

2010-04-21

arxiv.org/abs/1004.3621v1

Information Processing 80 (edited by S. H. Lavington), North-Holland, Amsterdam, 1980, 613-619

Mathematics

Numerical Analysis

Corrected and updated version of a paper first published in 1980. 13 pages. For further details see http://wwwmaths.anu.edu.

Scientific paper

We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by examples. The topics include: power series methods, use of halving identities, asymptotic expansions, continued fractions, recurrence relations, Newton's method, numerical contour integration, and the arithmetic-geometric mean. Most of the algorithms discussed are implemented in the MP package (arXiv:1004.3173).

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