DLMF:22.19.E2 (Q7176): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q12034 / rank
 
Normal rank
Property / Symbols used: Q12034 / qualifier
 
Defining formula:

θ ( t ) 𝜃 𝑡 {\displaystyle{\displaystyle\theta(t)}}

\theta(t)
Property / Symbols used: Q12034 / qualifier
 
xml-id: C22.S19.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12035 / rank
 
Normal rank
Property / Symbols used: Q12035 / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: Q12035 / qualifier
 
xml-id: C22.S19.XMD2.m1dec

Latest revision as of 15:39, 2 January 2020

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DLMF:22.19.E2
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    Statements

    sin ( 1 2 θ ( t ) ) = sin ( 1 2 α ) sn ( t + K , sin ( 1 2 α ) ) , 1 2 𝜃 𝑡 1 2 𝛼 Jacobi-elliptic-sn 𝑡 𝐾 1 2 𝛼 {\displaystyle{\displaystyle\sin\left(\tfrac{1}{2}\theta(t)\right)=\sin\left(% \frac{1}{2}\alpha\right)\operatorname{sn}\left(t+K,\sin\left(\tfrac{1}{2}% \alpha\right)\right),}}
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    DLMF:22.19.E2
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    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2adec
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    K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    C19.S2.E8.m1adec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2aadec
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    θ ( t ) 𝜃 𝑡 {\displaystyle{\displaystyle\theta(t)}}
    C22.S19.XMD1.m1adec
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    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    C22.S19.XMD2.m1dec
    0 references