DLMF:19.22.E9 (Q6447)

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DLMF:19.22.E9
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    Statements

    test
    4 π ⁢ R G ⁡ ( 0 , a 0 2 , g 0 2 ) = 1 M ⁡ ( a 0 , g 0 ) ⁢ ( a 0 2 - ∑ n = 0 ∞ 2 n - 1 ⁢ c n 2 ) = 1 M ⁡ ( a 0 , g 0 ) ⁢ ( a 1 2 - ∑ n = 2 ∞ 2 n - 1 ⁢ c n 2 ) , 4 𝜋 Carlson-integral-RG 0 superscript subscript 𝑎 0 2 superscript subscript 𝑔 0 2 1 arithmetic-geometric-mean subscript 𝑎 0 subscript 𝑔 0 superscript subscript 𝑎 0 2 superscript subscript 𝑛 0 superscript 2 𝑛 1 superscript subscript 𝑐 𝑛 2 1 arithmetic-geometric-mean subscript 𝑎 0 subscript 𝑔 0 superscript subscript 𝑎 1 2 superscript subscript 𝑛 2 superscript 2 𝑛 1 superscript subscript 𝑐 𝑛 2 {\displaystyle{\displaystyle\frac{4}{\pi}R_{G}\left(0,a_{0}^{2},g_{0}^{2}% \right)=\frac{1}{M\left(a_{0},g_{0}\right)}\left(a_{0}^{2}-\sum_{n=0}^{\infty}% 2^{n-1}c_{n}^{2}\right)=\frac{1}{M\left(a_{0},g_{0}\right)}\left(a_{1}^{2}-% \sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right),}}
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    DLMF:19.22.E9
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