DLMF:22.6.E9 (Q6943): Difference between revisions

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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.m1hdec

Revision as of 14:58, 2 January 2020

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DLMF:22.6.E9
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    Statements

    Defining formula
    sd ⁡ ( 2 ⁢ z , k ) = 2 ⁢ sd ⁡ ( z , k ) ⁢ cd ⁡ ( z , k ) ⁢ nd ⁡ ( z , k ) 1 + k 2 ⁢ k ′ 2 ⁢ sd 4 ⁡ ( z , k ) , Jacobi-elliptic-sd 2 𝑧 𝑘 2 Jacobi-elliptic-sd 𝑧 𝑘 Jacobi-elliptic-cd 𝑧 𝑘 Jacobi-elliptic-nd 𝑧 𝑘 1 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sd 4 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(2z,k\right)=\frac{2% \operatorname{sd}\left(z,k\right)\operatorname{cd}\left(z,k\right)% \operatorname{nd}\left(z,k\right)}{1+k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{% 4}}\left(z,k\right)},}}
    0 references
    DLMF id
    DLMF:22.6.E9
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m2abdec
    0 references
    Jacobian elliptic function
    Defining formula
    nd ⁡ ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m3abdec
    0 references
    Jacobian elliptic function
    Defining formula
    sd ⁡ ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m2abdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1hdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1hdec
    0 references
     
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