New proofs of Borwein-type algorithms for Pi
Jesús Guillera · Integral Transforms and Special Functions · 2016
We use a method of translation to recover Borweins' quadratic and quartic iterations. Then, by using the WZ-method, we obtain some initial values which lead to the limit 1/π. We use neither the modular theory nor the formula of Gauss that we used in another paper. Our proofs are short and self-contained.