DLMF:19.11.E13 (Q6288): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m2addec
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.m1kdec
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.m1ldec
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.m1adec

Latest revision as of 13:48, 2 January 2020

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DLMF:19.11.E13
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    Statements

    E ( ψ , k ) = 2 E ( θ , k ) - k 2 sin 2 θ sin ψ , elliptic-integral-second-kind-E 𝜓 𝑘 2 elliptic-integral-second-kind-E 𝜃 𝑘 superscript 𝑘 2 2 𝜃 𝜓 {\displaystyle{\displaystyle E\left(\psi,k\right)=2E\left(\theta,k\right)-k^{2% }{\sin^{2}}\theta\sin\psi,}}
    0 references
    DLMF:19.11.E13
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    E ( ϕ , k ) elliptic-integral-second-kind-E italic-ϕ 𝑘 {\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}
    C19.S2.E5.m2abdec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2addec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C19.S1.XMD5.m1kdec
    0 references
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    C19.S11.XMD1.m1ldec
    0 references
    ψ 𝜓 {\displaystyle{\displaystyle\psi}}
    C19.S11.XMD8.m1adec
    0 references