DLMF:19.8.E6 (Q6212): Difference between revisions

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Property / constraint
 

g 0 = k subscript 𝑔 0 superscript 𝑘 {\displaystyle{\displaystyle g_{0}=k^{\prime}}}

g_{0}=k^{\prime}
Property / constraint: g 0 = k subscript 𝑔 0 superscript 𝑘 {\displaystyle{\displaystyle g_{0}=k^{\prime}}} / rank
 
Normal rank

Revision as of 17:05, 30 December 2019

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DLMF:19.8.E6
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    Statements

    E ( k ) = π 2 M ( 1 , k ) ( a 0 2 - n = 0 2 n - 1 c n 2 ) = K ( k ) ( a 1 2 - n = 2 2 n - 1 c n 2 ) , complete-elliptic-integral-second-kind-E 𝑘 𝜋 2 arithmetic-geometric-mean 1 superscript 𝑘 superscript subscript 𝑎 0 2 superscript subscript 𝑛 0 superscript 2 𝑛 1 superscript subscript 𝑐 𝑛 2 complete-elliptic-integral-first-kind-K 𝑘 superscript subscript 𝑎 1 2 superscript subscript 𝑛 2 superscript 2 𝑛 1 superscript subscript 𝑐 𝑛 2 {\displaystyle{\displaystyle E\left(k\right)=\frac{\pi}{2M\left(1,k^{\prime}% \right)}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right)=K\left(k% \right)\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right),}}
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    g 0 = k subscript 𝑔 0 superscript 𝑘 {\displaystyle{\displaystyle g_{0}=k^{\prime}}}
    0 references