Application of a new iterative formula for computing $Ï$ and nested radicals with roots of $2$
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal, Brendan M. Quine
Published: 2025/9/24
Abstract
In this work, we obtain an iterative formula that can be used for computing digits of $\pi$ and nested radicals of kind $c_n/\sqrt{2 - c_{n - 1}}$, where $c_0 = 0$ and $c_n = \sqrt{2 + c_{n - 1}}$. We also show how with help of this iterative formula the two-term Machin-like formulas for $\pi$ can be generated and approximated. Some examples with Mathematica codes are presented.