Landen transformations and the integration of rational functions

Details Landen transformations and the integration of rational functions Landen transformations and the integration of rational functions

2007-07-26

arxiv.org/abs/0707.3910v1

Math. Comp. 71, 2002, 649-668

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

We present a rational version of the classical Landen transformation for
elliptic integrals. This is employed to obtain explicit closed-form expressions
for a large class of integrals of even rational functions and to develop an
algorithm for the numerical integration of these functions.

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