DLMF:22.13.E11 (Q7062): 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.m1kdec

Revision as of 15:19, 2 January 2020

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DLMF:22.13.E11
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    Statements

    Defining formula
    ( d d z ⁡ ds ⁡ ( z , k ) ) 2 = ( ds 2 ⁡ ( z , k ) - k ′ 2 ) ⁢ ( k 2 + ds 2 ⁡ ( z , k ) ) , superscript derivative 𝑧 Jacobi-elliptic-ds 𝑧 𝑘 2 Jacobi-elliptic-ds 2 𝑧 𝑘 superscript superscript 𝑘 ′ 2 superscript 𝑘 2 Jacobi-elliptic-ds 2 𝑧 𝑘 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% ds}\left(z,k\right)\right)^{2}=\left({\operatorname{ds}^{2}}\left(z,k\right)-{% k^{\prime}}^{2}\right)\left(k^{2}+{\operatorname{ds}^{2}}\left(z,k\right)% \right),}}
    0 references
    DLMF id
    DLMF:22.13.E11
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    ds ⁡ ( z , k ) Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m3aadec
    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.m2akdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1kdec
    0 references
     
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