An iterative method for computing $π$ by argument reduction of the tangent function
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913251313319936 |
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| author | Abrarov, Sanjar M. Siddiqui, Rehan Jagpal, Rajinder Kumar Quine, Brendan M. |
| author_facet | Abrarov, Sanjar M. Siddiqui, Rehan Jagpal, Rajinder Kumar Quine, Brendan M. |
| contents | In this work, we develop a new iterative method for computing the digits of $π$ by argument reduction of the tangent function. This method combines a modified version of the iterative formula for $π$ with squared convergence that we proposed in a previous work and a leading arctangent term from the Machin-like formula. The computational test we performed shows that algorithmic implementation can provide more than $17$ digits of $π$ per increment. Mathematica codes, showing the convergence rate for computing the digits of $π$, are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05413 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An iterative method for computing $π$ by argument reduction of the tangent function Abrarov, Sanjar M. Siddiqui, Rehan Jagpal, Rajinder Kumar Quine, Brendan M. General Mathematics 11Y60 In this work, we develop a new iterative method for computing the digits of $π$ by argument reduction of the tangent function. This method combines a modified version of the iterative formula for $π$ with squared convergence that we proposed in a previous work and a leading arctangent term from the Machin-like formula. The computational test we performed shows that algorithmic implementation can provide more than $17$ digits of $π$ per increment. Mathematica codes, showing the convergence rate for computing the digits of $π$, are presented. |
| title | An iterative method for computing $π$ by argument reduction of the tangent function |
| topic | General Mathematics 11Y60 |
| url | https://arxiv.org/abs/2312.05413 |