DLMF:19.34.E5 (Q6717)

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DLMF:19.34.E5
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    Statements

    Defining formula
    3 ⁢ c 2 8 ⁢ π ⁢ a ⁢ b ⁢ M = 3 ⁢ R F ⁡ ( 0 , r + 2 , r - 2 ) - 2 ⁢ r - 2 ⁢ R D ⁡ ( 0 , r + 2 , r - 2 ) , 3 speed-of-light 2 8 𝜋 𝑎 𝑏 𝑀 3 Carlson-integral-RF 0 superscript subscript 𝑟 2 superscript subscript 𝑟 2 2 superscript subscript 𝑟 2 Carlson-integral-RD 0 superscript subscript 𝑟 2 superscript subscript 𝑟 2 {\displaystyle{\displaystyle\frac{3{c^{2}}}{8\pi ab}M=3R_{F}\left(0,r_{+}^{2},% r_{-}^{2}\right)-2r_{-}^{2}R_{D}\left(0,r_{+}^{2},r_{-}^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.34.E5
    0 references
    Symbols used
    elliptic integral symmetric in only two variables
    Defining formula
    R D ⁡ ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E5.m2adec
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    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.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    Q11938
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C19.S34.XMD1.m1adec
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    Q11940
    Defining formula
    r ± subscript 𝑟 plus-or-minus {\displaystyle{\displaystyle r_{\pm}}}
    xml-id
    C19.S34.XMD3.m1bdec
    0 references
     
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