Self-replication and Borwein-like algorithms

Abstract

Using a self-replicating method, we generalize with a free parameter some Borwein algorithms for the number $\pi$. This generalization includes values of the Gamma function like $\Gamma (1/3)$, $\Gamma (1/4)$ and of course $\Gamma (1/2)=\sqrt{\pi }$. In addition, we give new rapid algorithms for the perimeter of an ellipse.

Some typos corrected (7 pages)

References in corpus (1)

• Crouching AGM, Hidden Modularity