DLMF:22.13.E5 (Q7056): 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:

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

\Jacobiellsdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E7.m2aadec

Revision as of 14:18, 2 January 2020

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DLMF:22.13.E5
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    Statements

    ( 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)},}}
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    sd ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E7.m2aadec
    0 references