DLMF:22.7.E6 (Q6963): 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:

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

\Jacobiellsnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E4.m2abdec

Revision as of 15:01, 2 January 2020

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DLMF:22.7.E6
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    Statements

    Defining formula
    sn ⁡ ( z , k ) = ( 1 + k 2 ′ ) ⁢ sn ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) ⁢ cn ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) dn ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) , Jacobi-elliptic-sn 𝑧 𝑘 1 superscript subscript 𝑘 2 ′ Jacobi-elliptic-sn 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 Jacobi-elliptic-cn 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 Jacobi-elliptic-dn 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 {\displaystyle{\displaystyle\operatorname{sn}\left(z,k\right)=\frac{(1+k_{2}^{% \prime})\operatorname{sn}\left(z/(1+k_{2}^{\prime}),k_{2}\right)\operatorname{% cn}\left(z/(1+k_{2}^{\prime}),k_{2}\right)}{\operatorname{dn}\left(z/(1+k_{2}^% {\prime}),k_{2}\right)},}}
    0 references
    DLMF id
    DLMF:22.7.E6
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2aadec
    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.m2abdec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2abdec
    0 references
     
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