DLMF:19.30.E13 (Q6688)

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DLMF:19.30.E13
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    Statements

    Defining formula
    P = 4 ⁢ 2 ⁢ a 2 ⁢ R F ⁡ ( 0 , 1 , 2 ) = 2 ⁢ a 2 × 5.24411 51 ⁢ … = 4 ⁢ a ⁢ K ⁡ ( 1 / 2 ) = a × 7.41629 87 ⁢ … . 𝑃 4 2 superscript 𝑎 2 Carlson-integral-RF 0 1 2 2 superscript 𝑎 2 5.24411 51 … 4 𝑎 complete-elliptic-integral-first-kind-K 1 2 𝑎 7.41629 87 … {\displaystyle{\displaystyle P=4\sqrt{2a^{2}}R_{F}\left(0,1,2\right)=\sqrt{2a^% {2}}\times 5.24411\;51\ldots=4aK\left(1/\sqrt{2}\right)=a\times 7.41629\;87% \dots.}}
    0 references
    DLMF id
    DLMF:19.30.E13
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2acdec
    0 references
     
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