DLMF:22.13.E5 (Q7056): Difference between revisions

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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.m1cdec

Latest revision as of 15:19, 2 January 2020

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DLMF:22.13.E5
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    Statements

    Defining formula
    ( d d z ⁡ sd ⁡ ( z , k ) ) 2 = ( 1 - k ′ 2 ⁢ sd 2 ⁡ ( z , k ) ) ⁢ ( 1 + k 2 ⁢ sd 2 ⁡ ( z , k ) ) , superscript derivative 𝑧 Jacobi-elliptic-sd 𝑧 𝑘 2 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sd 2 𝑧 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-sd 2 𝑧 𝑘 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% sd}\left(z,k\right)\right)^{2}={\left(1-{k^{\prime}}^{2}{\operatorname{sd}^{2}% }\left(z,k\right)\right)}{\left(1+k^{2}{\operatorname{sd}^{2}}\left(z,k\right)% \right)},}}
    0 references
    DLMF id
    DLMF:22.13.E5
    0 references
    Symbols used
    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.m2aadec
    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.m2aedec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1edec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1edec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1cdec
    0 references
     
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