Application of a new iterative formula for computing $π$ and nested radicals with roots of $2$

Sanjar M. Abrarov; Rehan Siddiqui; Rajinder Kumar Jagpal; Brendan M. Quine

doi:10.3390/appliedmath5040156

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arXiv · 2509.25221

Application of a new iterative formula for computing $π$ and nested radicals with roots of $2$

Sanjar M. Abrarov·Rehan Siddiqui·Rajinder Kumar Jagpal·Brendan M. Quine

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Abstract

In this work, we obtain an iterative formula that can be used for computing digits of $π$ 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 the help of this iterative formula, the two-term Machin-like formulas for $π$ can be generated and approximated. Some examples with Mathematica codes are presented.

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Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal, Brendan M. Quine. 2025-11-07. Application of a new iterative formula for computing $π$ and nested radicals with roots of $2$. https://doi.org/10.3390/appliedmath5040156

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