DLMF:22.6.E13 (Q6947): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1ldec

Revision as of 14:58, 2 January 2020

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DLMF:22.6.E13
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    Statements

    Defining formula
    sc ⁡ ( 2 ⁢ z , k ) = 2 ⁢ sc ⁡ ( z , k ) ⁢ dc ⁡ ( z , k ) ⁢ nc ⁡ ( z , k ) 1 - k ′ 2 ⁢ sc 4 ⁡ ( z , k ) , Jacobi-elliptic-sc 2 𝑧 𝑘 2 Jacobi-elliptic-sc 𝑧 𝑘 Jacobi-elliptic-dc 𝑧 𝑘 Jacobi-elliptic-nc 𝑧 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 4 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(2z,k\right)=\frac{2% \operatorname{sc}\left(z,k\right)\operatorname{dc}\left(z,k\right)% \operatorname{nc}\left(z,k\right)}{1-{k^{\prime}}^{2}{\operatorname{sc}^{4}}% \left(z,k\right)},}}
    0 references
    DLMF id
    DLMF:22.6.E13
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    dc ⁡ ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m3acdec
    0 references
    Jacobian elliptic function
    Defining formula
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3acdec
    0 references
    Jacobian elliptic function
    Defining formula
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2acdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1ldec
    0 references
     
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