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

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Property / Symbols used
 
Property / Symbols used: Q11849 / rank
 
Normal rank
Property / Symbols used: Q11849 / qualifier
 
Defining formula:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11849 / qualifier
 
xml-id: C19.S11.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: angle (locally) / rank
 
Normal rank
Property / Symbols used: angle (locally) / qualifier
 
Defining formula:

ψ 𝜓 {\displaystyle{\displaystyle\psi}}

\psi
Property / Symbols used: angle (locally) / qualifier
 
xml-id: C19.S11.XMD8.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11850 / rank
 
Normal rank
Property / Symbols used: Q11850 / qualifier
 
Defining formula:

γ 𝛾 {\displaystyle{\displaystyle\gamma}}

\gamma
Property / Symbols used: Q11850 / qualifier
 
xml-id: C19.S11.XMD9.m1dec

Latest 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
    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1ndec
    0 references
    Q11809
    Defining formula
    α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}
    xml-id
    C19.S1.XMD7.m1ddec
    0 references
    Q11842
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C19.S11.XMD1.m1odec
    0 references
    Q11849
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C19.S11.XMD10.m1dec
    0 references
    angle (locally)
    Defining formula
    ψ 𝜓 {\displaystyle{\displaystyle\psi}}
    xml-id
    C19.S11.XMD8.m1ddec
    0 references
    Q11850
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C19.S11.XMD9.m1dec
    0 references
     
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