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formula-elliptic-integral: $\text{agm}(a,b) = \frac{(a+b)\pi}{4K((a-b)/(a+b))}$, where $K(k) = \int_0^{\pi/2} \frac{d\theta}{\sqrt{1-k^2\sin^2\theta}}$ is the- complete elliptic integral of the first kind CITE{WikiEllInt}.+ HREF{Complete_elliptic_integral_of_the_first_kind_K}[complete elliptic integral+ of the first kind] CITE{WikiEllInt}. formula-symmetric: $\text{agm}(a,b) = \text{agm}(b,a)$ formula-diagonal: $\text{agm}(a,a) = a$
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