A simple example of a new class of Landen transformation

Details A simple example of a new class of Landen transformation A simple example of a new class of Landen transformation

2007-07-26

arxiv.org/abs/0707.3911v1

Amer. Math. Monthly 114, 2007, 232-241

Mathematics

Classical Analysis and ODEs

12 pages

Scientific paper

The rational Landen transformation is a map on the coefficients of a rational
integrand that preserves the value of the integral. This is the rational analog
of the classical Landen transformations for elliptic integrals that leads to
the arithmetic-geometric mean of Legendre and Gauss. We present the effect of
this transformation in the simplest possible case.

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