DLMF:22.16.E17 (Q7137): 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:

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

\Jacobielldnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m2aadec

Revision as of 15:33, 2 January 2020

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DLMF:22.16.E17
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    Statements

    Defining formula
    ℰ ⁡ ( x , k ) = ∫ 0 x dn 2 ⁡ ( t , k ) ⁢ d t . Jacobi-Epsilon 𝑥 𝑘 superscript subscript 0 𝑥 Jacobi-elliptic-dn 2 𝑡 𝑘 𝑡 {\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=\int_{0}^{x}{% \operatorname{dn}^{2}}\left(t,k\right)\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:22.16.E17
    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.m2acdec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2aadec
    0 references
     
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