Gauss–Legendre algorithm: Difference between revisions

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=== Legendre’s identity ===
 
For <math>\varphi\!</math> and <math>\theta\!</math> such that <math>\varphi+\theta={1 \over 2}\pi\!</math> Legendre proved the identity:
:<math>K(\sin \varphi) E(\sin \theta ) + K(\sin \theta ) E(\sin \varphi) - K(\sin \varphi) K(\sin \theta) = {1 \over 2}\pi.\!</math><ref name="brent" />
 
=== Gauss–Legendre method ===