DLMF:19.11.E16 (Q6295): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / rank
 
Normal rank
Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / qualifier
 
Defining formula:

Π ⁡ ( ϕ , α 2 , k ) elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 𝑘 {\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}% \right)}}

\incellintPik@{\NVar{\phi}}{\NVar{\alpha}^{2}}{\NVar{k}}
Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / qualifier
 
xml-id: C19.S2.E7.m2abdec

Revision as of 13:49, 2 January 2020

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DLMF:19.11.E16
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    Statements

    Defining formula
    Π ⁡ ( ψ , α 2 , k ) = 2 ⁢ Π ⁡ ( θ , α 2 , k ) + α 2 ⁢ R C ⁡ ( γ - δ , γ ) , elliptic-integral-third-kind-Pi 𝜓 superscript 𝛼 2 𝑘 2 elliptic-integral-third-kind-Pi 𝜃 superscript 𝛼 2 𝑘 superscript 𝛼 2 Carlson-integral-RC 𝛾 𝛿 𝛾 {\displaystyle{\displaystyle\Pi\left(\psi,\alpha^{2},k\right)=2\Pi\left(\theta% ,\alpha^{2},k\right)+\alpha^{2}R_{C}\left(\gamma-\delta,\gamma\right),}}
    0 references
    DLMF id
    DLMF:19.11.E16
    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.m2abdec
    0 references
    Legendre’s incomplete elliptic integral of the third kind
    Defining formula
    Π ⁡ ( ϕ , α 2 , k ) elliptic-integral-third-kind-Pi italic-ϕ superscript 𝛼 2 𝑘 {\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}% \right)}}
    xml-id
    C19.S2.E7.m2abdec
    0 references
     
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