DLMF:19.11.E10 (Q6284): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11809 / rank
 
Normal rank
Property / Symbols used: Q11809 / qualifier
 
Defining formula:

α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}

\alpha^{2}
Property / Symbols used: Q11809 / qualifier
 
xml-id: C19.S1.XMD7.m1bdec

Revision as of 13:48, 2 January 2020

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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
    Q11816
    Defining formula
    Π ⁡ ( α 2 , k ) complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 {\displaystyle{\displaystyle\Pi\left(\NVar{\alpha}^{2},\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m4adec
    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.m2aadec
    0 references
    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1idec
    0 references
    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1hdec
    0 references
    Q11809
    Defining formula
    α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}
    xml-id
    C19.S1.XMD7.m1bdec
    0 references
     
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