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An iterative method for computing $\pi$ by argument reduction of the tangent function
- Source :
- Math. Comput. Appl. 2024, 29(2), 17
- Publication Year :
- 2023
-
Abstract
- In this work, we develop a new iterative method for computing the digits of $\pi$ by argument reduction of the tangent function. This method combines a modified version of the iterative formula for $\pi$ 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 $\pi$ per increment. Mathematica codes, showing the convergence rate for computing the digits of $\pi$, are presented.<br />Comment: 35 pages
- Subjects :
- Mathematics - General Mathematics
11Y60
Subjects
Details
- Database :
- arXiv
- Journal :
- Math. Comput. Appl. 2024, 29(2), 17
- Publication Type :
- Report
- Accession number :
- edsarx.2312.05413
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3390/mca29020017