DLMF:19.8.E4 (Q6210): Difference between revisions

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DLMF:19.8.E4
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    1 M ( a 0 , g 0 ) = 2 π 0 π / 2 d θ a 0 2 cos 2 θ + g 0 2 sin 2 θ = 1 π 0 d t t ( t + a 0 2 ) ( t + g 0 2 ) . 1 arithmetic-geometric-mean subscript 𝑎 0 subscript 𝑔 0 2 𝜋 superscript subscript 0 𝜋 2 𝜃 superscript subscript 𝑎 0 2 2 𝜃 superscript subscript 𝑔 0 2 2 𝜃 1 𝜋 superscript subscript 0 𝑡 𝑡 𝑡 superscript subscript 𝑎 0 2 𝑡 superscript subscript 𝑔 0 2 {\displaystyle{\displaystyle\frac{1}{M\left(a_{0},g_{0}\right)}=\frac{2}{\pi}% \int_{0}^{\pi/2}\frac{\mathrm{d}\theta}{\sqrt{a_{0}^{2}{\cos^{2}}\theta+g_{0}^% {2}{\sin^{2}}\theta}}=\frac{1}{\pi}\int_{0}^{\infty}\frac{\mathrm{d}t}{\sqrt{t% (t+a_{0}^{2})(t+g_{0}^{2})}}.}}
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    DLMF:19.8.E4
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