Rational Landen transformations on the real line
arXiv:0707.3862 · doi:10.1090/S0025-5718-07-01954-0
Abstract
The rational Landen transformation is a map on the space of coefficients of a rational integrand that preserves the value of the integral. We provide a family of these transformations that apply to rational integrands on the whole line. Given an integer m, these transformations produce a numerical scheme to evaluate the integral that is of order m.
22 pages