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A new form of the Machin-like formula for \(\pi\) by iteration with increasing integers. (English) Zbl 1495.11147

Summary: 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 \(k \geq 17\), the Lehmer measure remains small and practically does not increase after 18 steps of iteration.

MSC:

11Y60 Evaluation of number-theoretic constants

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Online Encyclopedia of Integer Sequences:

Decimal expansion of arccot(10).

References:

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