DLMF:19.30.E5 (Q6679)

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DLMF:19.30.E5
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    Statements

    Defining formula
    L ⁢ ( a , b ) = 4 ⁢ a ⁢ E ⁡ ( k ) = 8 ⁢ a ⁢ R G ⁡ ( 0 , b 2 / a 2 , 1 ) = 8 ⁢ R G ⁡ ( 0 , a 2 , b 2 ) = 8 ⁢ a ⁢ b ⁢ R G ⁡ ( 0 , a - 2 , b - 2 ) , 𝐿 𝑎 𝑏 4 𝑎 complete-elliptic-integral-second-kind-E 𝑘 8 𝑎 Carlson-integral-RG 0 superscript 𝑏 2 superscript 𝑎 2 1 8 Carlson-integral-RG 0 superscript 𝑎 2 superscript 𝑏 2 8 𝑎 𝑏 Carlson-integral-RG 0 superscript 𝑎 2 superscript 𝑏 2 {\displaystyle{\displaystyle L(a,b)=4aE\left(k\right)=8aR_{G}\left(0,b^{2}/a^{% 2},1\right)=8R_{G}\left(0,a^{2},b^{2}\right)=8abR_{G}\left(0,a^{-2},b^{-2}% \right),}}
    0 references
    DLMF id
    DLMF:19.30.E5
    0 references
    Symbols used
    symmetric elliptic integral of second kind
    Defining formula
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2adec
    0 references
     
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