Easy Proofs of Some Borwein Algorithms for $\pi$
Number Theory
2008-03-10 v1 Classical Analysis and ODEs
Abstract
In 1987 Jonathan and Peter Borwein, inspired by the works of Ramanujan, derived many efficient algorithms for computing . We will see that by using only a formula of Gauss's and elementary algebra we are able to prove the correctness of two of them.
Keywords
Cite
@article{arxiv.0803.0991,
title = {Easy Proofs of Some Borwein Algorithms for $\pi$},
author = {Jesus Guillera},
journal= {arXiv preprint arXiv:0803.0991},
year = {2008}
}
Comments
To appear in The American Mathematical Monthly. (6 pages)