DLMF:19.11.E2 (Q6272): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Legendre’s incomplete elliptic integral of the second kind / rank
 
Normal rank
Property / Symbols used: Legendre’s incomplete elliptic integral of the second kind / qualifier
 
Defining formula:

E ⁡ ( ϕ , k ) elliptic-integral-second-kind-E italic-ϕ 𝑘 {\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}

\incellintEk@{\NVar{\phi}}{\NVar{k}}
Property / Symbols used: Legendre’s incomplete elliptic integral of the second kind / qualifier
 
xml-id: C19.S2.E5.m2adec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11807 / rank
 
Normal rank
Property / Symbols used: Q11807 / qualifier
 
Defining formula:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: Q11807 / qualifier
 
xml-id: C19.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11808 / rank
 
Normal rank
Property / Symbols used: Q11808 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1adec
Property / Symbols used
 
Property / Symbols used: Q11842 / rank
 
Normal rank
Property / Symbols used: Q11842 / qualifier
 
Defining formula:

θ 𝜃 {\displaystyle{\displaystyle\theta}}

\theta
Property / Symbols used: Q11842 / qualifier
 
xml-id: C19.S11.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11843 / rank
 
Normal rank
Property / Symbols used: Q11843 / qualifier
 
Defining formula:

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

\psi
Property / Symbols used: Q11843 / qualifier
 
xml-id: C19.S11.XMD2.m1adec

Latest revision as of 13:47, 2 January 2020

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DLMF:19.11.E2
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    Statements

    Defining formula
    E ⁡ ( θ , k ) + E ⁡ ( ϕ , k ) = E ⁡ ( ψ , k ) + k 2 ⁢ sin ⁡ θ ⁢ sin ⁡ ϕ ⁢ sin ⁡ ψ . elliptic-integral-second-kind-E 𝜃 𝑘 elliptic-integral-second-kind-E italic-ϕ 𝑘 elliptic-integral-second-kind-E 𝜓 𝑘 superscript 𝑘 2 𝜃 italic-ϕ 𝜓 {\displaystyle{\displaystyle E\left(\theta,k\right)+E\left(\phi,k\right)=E% \left(\psi,k\right)+k^{2}\sin\theta\sin\phi\sin\psi.}}
    0 references
    DLMF id
    DLMF:19.11.E2
    0 references
    Symbols used
    Legendre’s incomplete elliptic integral of the second kind
    Defining formula
    E ⁡ ( ϕ , k ) elliptic-integral-second-kind-E italic-ϕ 𝑘 {\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}
    xml-id
    C19.S2.E5.m2adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1adec
    0 references
    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1adec
    0 references
    Q11842
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C19.S11.XMD1.m1adec
    0 references
    Q11843
    Defining formula
    ψ 𝜓 {\displaystyle{\displaystyle\psi}}
    xml-id
    C19.S11.XMD2.m1adec
    0 references
     
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