Computation of $\pi$ using arithmetic-geometric mean
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- by Eugene Salamin PDF
- Math. Comp. 30 (1976), 565-570 Request permission
Abstract:
A new formula for $\pi$ is derived. It is a direct consequence of Gauss’ arithmetic-geometric mean, the traditional method for calculating elliptic integrals, and of Legendre’s relation for elliptic integrals. The error analysis shows that its rapid convergence doubles the number of significant digits after each step. The new formula is proposed for use in a numerical computation of $\pi$, but no actual computational results are reported here.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 565-570
- MSC: Primary 10A30; Secondary 10A40, 33A25
- DOI: https://doi.org/10.1090/S0025-5718-1976-0404124-9
- MathSciNet review: 0404124