DLMF:19.11.E10 (Q6284)

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DLMF:19.11.E10
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    Statements

    Defining formula
    Π ⁡ ( ϕ , α 2 , k ) = Π ⁡ ( α 2 , k ) - Π ⁡ ( θ , α 2 , k ) - α 2 ⁢ R C ⁡ ( γ - δ , γ ) , elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 𝑘 complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 elliptic-integral-third-kind-Pi 𝜃 superscript 𝛼 2 𝑘 superscript 𝛼 2 Carlson-integral-RC 𝛾 𝛿 𝛾 {\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},k\right)=\Pi\left(\alpha^% {2},k\right)-\Pi\left(\theta,\alpha^{2},k\right)-\alpha^{2}R_{C}\left(\gamma-% \delta,\gamma\right),}}
    0 references
    DLMF id
    DLMF:19.11.E10
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    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.m2aadec
    0 references
     
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