DLMF:22.13.E6 (Q7057): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m1fdec

Revision as of 15:19, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.13.E6
No description defined

    Statements

    Defining formula
    ( d d z ⁡ nd ⁡ ( z , k ) ) 2 = ( nd 2 ⁡ ( z , k ) - 1 ) ⁢ ( 1 - k ′ 2 ⁢ nd 2 ⁡ ( z , k ) ) , superscript derivative 𝑧 Jacobi-elliptic-nd 𝑧 𝑘 2 Jacobi-elliptic-nd 2 𝑧 𝑘 1 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-nd 2 𝑧 𝑘 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% nd}\left(z,k\right)\right)^{2}=\left({\operatorname{nd}^{2}}\left(z,k\right)-1% \right)\left(1-{k^{\prime}}^{2}{\operatorname{nd}^{2}}\left(z,k\right)\right),}}
    0 references
    DLMF id
    DLMF:22.13.E6
    0 references
    Symbols used
    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.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.m2afdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1fdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7057&oldid=56562"