DLMF:19.23.E7 (Q6478): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of second kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of second kind / qualifier
 
test:

R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

\CarlsonsymellintRG@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of second kind / qualifier
 
xml-id: C19.S16.E3.m2aadec

Revision as of 13:02, 2 January 2020

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DLMF:19.23.E7
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    Statements

    test
    R G ⁡ ( x , y , z ) = 1 4 ⁢ ∫ 0 ∞ 1 t + x ⁢ t + y ⁢ t + z ⁢ ( x t + x + y t + y + z t + z ) ⁢ t ⁢ d t , Carlson-integral-RG 𝑥 𝑦 𝑧 1 4 superscript subscript 0 1 𝑡 𝑥 𝑡 𝑦 𝑡 𝑧 𝑥 𝑡 𝑥 𝑦 𝑡 𝑦 𝑧 𝑡 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle R_{G}\left(x,y,z\right)=\frac{1}{4}\int_{0}^{% \infty}\frac{1}{\sqrt{t+x}\sqrt{t+y}\sqrt{t+z}}\*\left(\frac{x}{t+x}+\frac{y}{% t+y}+\frac{z}{t+z}\right)t\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:19.23.E7
    0 references
    constraint
    x , y , z ∈ ℂ ∖ ( - ∞ , 0 ] 𝑥 𝑦 𝑧 0 {\displaystyle{\displaystyle x,y,z\in\mathbb{C}\setminus(-\infty,0]}}
    0 references
    Symbols used
    symmetric elliptic integral of second kind
    test
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2aadec
    0 references
     
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