Rational Landen transformations on the real line

TL;DR

This paper introduces a family of rational Landen transformations on the real line that preserve integrals and offer a numerical scheme of order m for evaluating rational integrals.

Contribution

It develops a new class of transformations for rational integrals on the entire real line, enabling high-order numerical evaluation schemes.

Findings

Transformations preserve the value of rational integrals.

Numerical schemes of arbitrary order m are constructed.

Applicable to integrals over the entire real line.

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.