A formula which uses the Arithmetic-Geometric Mean to compute Pi. It has quadratic convergence and
is also called the Gauss-Salamin Formula and Salamin Formula. Let
(1) | |||
(2) | |||
(3) | |||
(4) |
(5) | |||
(6) |
See also Arithmetic-Geometric Mean, Pi
References
Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity.
New York: Wiley, pp. 48-51, 1987.
Castellanos, D. ``The Ubiquitous Pi. Part II.'' Math. Mag. 61, 148-163, 1988.
King, L. V. On the Direct Numerical Calculation of Elliptic Functions and Integrals. Cambridge, England: Cambridge University Press, 1924.
Lord, N. J. ``Recent Calculations of : The Gauss-Salamin Algorithm.'' Math. Gaz. 76, 231-242, 1992.
Salamin, E. ``Computation of Using Arithmetic-Geometric Mean.'' Math. Comput. 30, 565-570, 1976.