DLMF:22.6.E5 (Q6939): Difference between revisions

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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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1ddec

Latest revision as of 14:57, 2 January 2020

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DLMF:22.6.E5
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    Statements

    Defining formula
    sn ⁡ ( 2 ⁢ z , k ) = 2 ⁢ sn ⁡ ( z , k ) ⁢ cn ⁡ ( z , k ) ⁢ dn ⁡ ( z , k ) 1 - k 2 ⁢ sn 4 ⁡ ( z , k ) , Jacobi-elliptic-sn 2 𝑧 𝑘 2 Jacobi-elliptic-sn 𝑧 𝑘 Jacobi-elliptic-cn 𝑧 𝑘 Jacobi-elliptic-dn 𝑧 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-sn 4 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(2z,k\right)=\frac{2% \operatorname{sn}\left(z,k\right)\operatorname{cn}\left(z,k\right)% \operatorname{dn}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z,k% \right)},}}
    0 references
    DLMF id
    DLMF:22.6.E5
    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.m2aadec
    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.m2aadec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1ddec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1ddec
    0 references
     
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