DLMF:22.16.E20 (Q7140): 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:

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

\Jacobiellndk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m3adec

Revision as of 15:34, 2 January 2020

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DLMF:22.16.E20
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    Statements

    Defining formula
    ℰ ⁡ ( x , k ) = k ′ 2 ⁢ ∫ 0 x nd 2 ⁡ ( t , k ) ⁢ d t + k 2 ⁢ sn ⁡ ( x , k ) ⁢ cd ⁡ ( x , k ) . Jacobi-Epsilon 𝑥 𝑘 superscript superscript 𝑘 ′ 2 superscript subscript 0 𝑥 Jacobi-elliptic-nd 2 𝑡 𝑘 𝑡 superscript 𝑘 2 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-cd 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)={k^{\prime}}^{2}\int_{% 0}^{x}{\operatorname{nd}^{2}}\left(t,k\right)\mathrm{d}t+k^{2}\operatorname{sn% }\left(x,k\right)\operatorname{cd}\left(x,k\right).}}
    0 references
    DLMF id
    DLMF:22.16.E20
    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.m2afdec
    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.m2abdec
    0 references
    Jacobian elliptic function
    Defining formula
    nd ⁡ ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m3adec
    0 references
     
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