DLMF:19.19.E6 (Q6366)

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DLMF:19.19.E6
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    Statements

    Defining formula
    R J ⁡ ( x , y , z , p ) = R - 3 2 ⁡ ( 1 2 , 1 2 , 1 2 , 1 2 , 1 2 ; x , y , z , p , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 Carlson-integral-R 3 2 1 2 1 2 1 2 1 2 1 2 𝑥 𝑦 𝑧 𝑝 𝑝 {\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)=R_{-\frac{3}{2}}\left(% \tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2};x,y,z,p,p% \right)}}
    0 references
    DLMF id
    DLMF:19.19.E6
    0 references
    Symbols used
    multivariate hypergeometric function
    Defining formula
    R - a ⁡ ( b 1 , … , b n ; z 1 , … , z n ) Carlson-integral-R 𝑎 subscript 𝑏 1 … subscript 𝑏 𝑛 subscript 𝑧 1 … subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
    xml-id
    C19.S16.E9.m2abdec
    0 references
    symmetric elliptic integral of third kind
    Defining formula
    R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    xml-id
    C19.S16.E2.m2adec
    0 references
     
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