DLMF:19.20.E3 (Q6377)

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DLMF:19.20.E3
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    Statements

    Defining formula
    R F ⁡ ( x , a , y ) = R - 1 4 ⁡ ( 3 4 , 1 2 ; a 2 , x ⁢ y ) , Carlson-integral-RF 𝑥 𝑎 𝑦 Carlson-integral-R 1 4 3 4 1 2 superscript 𝑎 2 𝑥 𝑦 {\displaystyle{\displaystyle R_{F}\left(x,a,y\right)=R_{-\frac{1}{4}}\left(% \tfrac{3}{4},\tfrac{1}{2};a^{2},xy\right),}}
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    DLMF id
    DLMF:19.20.E3
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    constraint
    a = 1 2 ⁢ ( x + y ) 𝑎 1 2 𝑥 𝑦 {\displaystyle{\displaystyle a=\frac{1}{2}(x+y)}}
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    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.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.m2abdec
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