English

New proofs of Borwein-type algorithms for Pi

Number Theory 2016-04-04 v1

Abstract

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/π1/\pi. We will not use the modular theory nor either the Gauss' formula that we used in another paper. Our proofs are short and self-contained.

Keywords

Cite

@article{arxiv.1604.00193,
  title  = {New proofs of Borwein-type algorithms for Pi},
  author = {Jesús Guillera},
  journal= {arXiv preprint arXiv:1604.00193},
  year   = {2016}
}

Comments

8 pages

R2 v1 2026-06-22T13:23:09.460Z