DLMF:22.13.E10 (Q7061): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

ns ( z , k ) Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellnsk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E4.m3aadec

Revision as of 15:19, 2 January 2020

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DLMF:22.13.E10
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    Statements

    ( d d z ns ( z , k ) ) 2 = ( ns 2 ( z , k ) - k 2 ) ( ns 2 ( z , k ) - 1 ) , superscript derivative 𝑧 Jacobi-elliptic-ns 𝑧 𝑘 2 Jacobi-elliptic-ns 2 𝑧 𝑘 superscript 𝑘 2 Jacobi-elliptic-ns 2 𝑧 𝑘 1 {\displaystyle{\displaystyle\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% ns}\left(z,k\right)\right)^{2}=\left({\operatorname{ns}^{2}}\left(z,k\right)-k% ^{2}\right)\left({\operatorname{ns}^{2}}\left(z,k\right)-1\right),}}
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    ns ( z , k ) Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m3aadec
    0 references