DLMF:19.26.E9 (Q7257)

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DLMF:19.26.E9
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    Statements

    DLMF defining formula
    R J ⁡ ( x + λ , y + λ , z + λ , p + λ ) + R J ⁡ ( x + μ , y + μ , z + μ , p + μ ) = R J ⁡ ( x , y , z , p ) - 3 ⁢ R C ⁡ ( γ - δ , γ ) , Carlson-integral-RJ 𝑥 𝜆 𝑦 𝜆 𝑧 𝜆 𝑝 𝜆 Carlson-integral-RJ 𝑥 𝜇 𝑦 𝜇 𝑧 𝜇 𝑝 𝜇 Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 3 Carlson-integral-RC 𝛾 𝛿 𝛾 {\displaystyle{\displaystyle R_{J}\left(x+\lambda,y+\lambda,z+\lambda,p+% \lambda\right)+R_{J}\left(x+\mu,y+\mu,z+\mu,p+\mu\right)=R_{J}\left(x,y,z,p% \right)-3R_{C}\left(\gamma-\delta,\gamma\right),}}
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    DLMF defining formula
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2adec
    0 references
    symmetric elliptic integral of third kind
    DLMF 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
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    positive
    DLMF defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C19.S26.XMD1.m1gdec
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    δ
    DLMF defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C19.S26.XMD10.m1dec
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    positive
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C19.S26.XMD2.m1gdec
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    positive
    DLMF defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C19.S26.XMD3.m1gdec
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    positive
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C19.S26.XMD4.m1hdec
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    parameter
    DLMF defining formula
    μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}}
    xml-id
    C19.S26.XMD5.m1gdec
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    γ
    DLMF defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C19.S26.XMD9.m1dec
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    Identifiers

     
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