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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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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