DLMF:22.7.E8 (Q6965): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11989 / rank
 
Normal rank
Property / Symbols used: Q11989 / qualifier
 
Defining formula:

k 2 subscript 𝑘 2 {\displaystyle{\displaystyle k_{2}}}

k_{2}
Property / Symbols used: Q11989 / qualifier
 
xml-id: C22.S7.XMD2.m1cdec

Revision as of 15:01, 2 January 2020

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DLMF:22.7.E8
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    Statements

    Defining formula
    dn ⁡ ( z , k ) = ( 1 - k 2 ′ ) ⁢ ( dn 2 ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) + k 2 ′ ) k 2 2 ⁢ dn ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) . Jacobi-elliptic-dn 𝑧 𝑘 1 superscript subscript 𝑘 2 ′ Jacobi-elliptic-dn 2 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 superscript subscript 𝑘 2 ′ superscript subscript 𝑘 2 2 Jacobi-elliptic-dn 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 {\displaystyle{\displaystyle\operatorname{dn}\left(z,k\right)=\frac{(1-k_{2}^{% \prime})({\operatorname{dn}^{2}}\left(z/(1+k_{2}^{\prime}),k_{2}\right)+k_{2}^% {\prime})}{k_{2}^{2}\operatorname{dn}\left(z/(1+k_{2}^{\prime}),k_{2}\right)}.}}
    0 references
    DLMF id
    DLMF:22.7.E8
    0 references
    Symbols used
    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.m2addec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1edec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1fdec
    0 references
    Q11989
    Defining formula
    k 2 subscript 𝑘 2 {\displaystyle{\displaystyle k_{2}}}
    xml-id
    C22.S7.XMD2.m1cdec
    0 references
     
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