Landen transformations and the integration of rational functions
George Boros, Victor H. Moll
TL;DR
This paper introduces a rational Landen transformation for elliptic integrals, enabling explicit formulas for integrals of even rational functions and an algorithm for their numerical integration.
Contribution
It develops a rational version of the Landen transformation and applies it to derive explicit integrals and a numerical algorithm for even rational functions.
Findings
Explicit closed-form expressions for integrals of even rational functions.
A new algorithm for numerical integration of these functions.
Extension of classical Landen transformation to rational functions.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematics and Applications · Advanced Combinatorial Mathematics · Mathematical functions and polynomials