DLMF:22.16.E28 (Q7148): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellcdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E8.m2acdec

Revision as of 15:36, 2 January 2020

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DLMF:22.16.E28
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    Statements

    Defining formula
    ℰ ⁡ ( x + K , k ) = ℰ ⁡ ( x , k ) + E ⁡ ( k ) - k 2 ⁢ sn ⁡ ( x , k ) ⁢ cd ⁡ ( x , k ) , Jacobi-Epsilon 𝑥 𝐾 𝑘 Jacobi-Epsilon 𝑥 𝑘 complete-elliptic-integral-second-kind-E 𝑘 superscript 𝑘 2 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-cd 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(x+K,k\right)=\mathcal{E}\left(x,k% \right)+E\left(k\right)-k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd% }\left(x,k\right),}}
    0 references
    DLMF id
    DLMF:22.16.E28
    0 references
    Symbols used
    Jacobi’s epsilon function
    Defining formula
    ℰ ⁡ ( x , k ) Jacobi-Epsilon 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S16.E14.m2andec
    0 references
    Jacobian elliptic function
    Defining formula
    cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m2acdec
    0 references
     
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