DLMF:22.13.E14 (Q7065): 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.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11988 / rank
 
Normal rank
Property / Symbols used: Q11988 / qualifier
 
Defining formula:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11988 / qualifier
 
xml-id: C22.S1.XMD5.m1idec

Latest revision as of 15:20, 2 January 2020

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DLMF:22.13.E14
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    Statements

    Defining formula
    d 2 d z 2 ⁡ cn ⁡ ( z , k ) = - ( k ′ 2 - k 2 ) ⁢ cn ⁡ ( z , k ) - 2 ⁢ k 2 ⁢ cn 3 ⁡ ( z , k ) , derivative 𝑧 2 Jacobi-elliptic-cn 𝑧 𝑘 superscript superscript 𝑘 ′ 2 superscript 𝑘 2 Jacobi-elliptic-cn 𝑧 𝑘 2 superscript 𝑘 2 Jacobi-elliptic-cn 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{cn}\left(z,k\right)=-({k^{\prime}}^{2}-k^{2})\operatorname{cn}% \left(z,k\right)-2k^{2}{\operatorname{cn}^{3}}\left(z,k\right),}}
    0 references
    DLMF id
    DLMF:22.13.E14
    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.m2abdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2andec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1ndec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1ndec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1idec
    0 references
     
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