Computation of it Using Arithmetic-Geometric Mean

@inproceedings{Salamin2010ComputationOI,
  title={Computation of it Using Arithmetic-Geometric Mean},
  author={Eugene Salamin},
  year={2010}
}
  • Eugene Salamin
  • Published 2010
A new formula for rr 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 n, but no actual computational results are reported here. 
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