Easy Proofs of Some Borwein Algorithms for
arXiv:0803.0991
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.
To appear in The American Mathematical Monthly. (6 pages)