DLMF:19.25.E13 (Q6517)

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DLMF:19.25.E13
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    Statements

    test
    D ⁡ ( ϕ , k ) = 1 3 ⁢ R D ⁡ ( c - 1 , c - k 2 , c ) . elliptic-integral-third-kind-D italic-ϕ 𝑘 1 3 Carlson-integral-RD 𝑐 1 𝑐 superscript 𝑘 2 𝑐 {\displaystyle{\displaystyle D\left(\phi,k\right)=\tfrac{1}{3}R_{D}\left(c-1,c% -k^{2},c\right).}}
    0 references
    DLMF id
    DLMF:19.25.E13
    0 references
    Symbols used
    elliptic integral symmetric in only two variables
    test
    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.m2afdec
    0 references
    incomplete elliptic integral of Legendre’s type
    test
    D ⁡ ( ϕ , k ) elliptic-integral-third-kind-D italic-ϕ 𝑘 {\displaystyle{\displaystyle D\left(\NVar{\phi},\NVar{k}\right)}}
    xml-id
    C19.S2.E6.m2adec
    0 references
     
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