A new form of the Machin-like formula for pi by iteration with increasing integers

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

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arXiv · 2108.07718

A new form of the Machin-like formula for pi by iteration with increasing integers

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

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Abstract

We present a new form of the Machin-like formula for $\pi$ that can be generated by using iteration. This form of the Machin-like formula may be promising for computation of the constant $\pi$ due to rapidly increasing integers at each step of the iteration. The computational test we performed shows that, with an integer $k \ge 17$, the Lehmer measure remains small and practically does not increase after $18$ steps of iteration.

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Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal, Brendan M. Quine. 2021-08-09. A new form of the Machin-like formula for pi by iteration with increasing integers. https://arxiv.org/abs/2108.07718

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