DLMF:19.18.E10 (Q6353)

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DLMF:19.18.E10
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    Statements

    Defining formula
    ( ( x - y ) ⁢ ∂ 2 ⁡ ∂ ⁡ x ⁢ ∂ ⁡ y + 1 2 ⁢ ( ∂ ∂ ⁡ y - ∂ ∂ ⁡ x ) ) ⁢ R F ⁡ ( x , y , z ) = 0 , 𝑥 𝑦 2 𝑥 𝑦 1 2 partial-derivative 𝑦 partial-derivative 𝑥 Carlson-integral-RF 𝑥 𝑦 𝑧 0 {\displaystyle{\displaystyle\left((x-y)\frac{{\partial}^{2}}{\partial x% \partial y}+\frac{1}{2}\left(\frac{\partial}{\partial y}-\frac{\partial}{% \partial x}\right)\right)R_{F}\left(x,y,z\right)=0,}}
    0 references
    DLMF id
    DLMF:19.18.E10
    0 references
    Symbols used
    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.m2aedec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4addec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2agdec
    0 references
     
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