A set of the Viète-like recurrence relations for the unity constant

Abstract

Using a simple Viète-like formula for $\pi$ based on the nested radicals $a_k=\sqrt{2+a_{k-1}}$ and $a_1=\sqrt{2}$, we derive a set of the recurrence relations for the constant $1$. Computational test shows that application of this set of the Viète-like recurrence relations results in a rapid convergence to unity.

9 pages, 1 figure, 1 table