DLMF:22.14.E9 (Q7084): 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:

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

\Jacobiellnck@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E5.m3abdec

Revision as of 14:24, 2 January 2020

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DLMF:22.14.E9
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    sc ( x , k ) d x = k - 1 ln ( dc ( x , k ) + k nc ( x , k ) ) . Jacobi-elliptic-sc 𝑥 𝑘 𝑥 superscript superscript 𝑘 1 Jacobi-elliptic-dc 𝑥 𝑘 superscript 𝑘 Jacobi-elliptic-nc 𝑥 𝑘 {\displaystyle{\displaystyle\int\operatorname{sc}\left(x,k\right)\mathrm{d}x={% k^{\prime}}^{-1}\ln\left(\operatorname{dc}\left(x,k\right)+k^{\prime}% \operatorname{nc}\left(x,k\right)\right).}}
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    dc ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E8.m3abdec
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    nc ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E5.m3abdec
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