DLMF:22.14.E14 (Q7089): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12003 / rank
 
Normal rank
Property / Symbols used: Q12003 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12003 / qualifier
 
xml-id: C22.S1.XMD1.m1mdec

Revision as of 15:25, 2 January 2020

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DLMF:22.14.E14
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    Statements

    cn ( x , k ) d x sn ( x , k ) = 1 2 ln ( 1 - dn ( x , k ) 1 + dn ( x , k ) ) , Jacobi-elliptic-cn 𝑥 𝑘 𝑥 Jacobi-elliptic-sn 𝑥 𝑘 1 2 1 Jacobi-elliptic-dn 𝑥 𝑘 1 Jacobi-elliptic-dn 𝑥 𝑘 {\displaystyle{\displaystyle\int\frac{\operatorname{cn}\left(x,k\right)\mathrm% {d}x}{\operatorname{sn}\left(x,k\right)}=\frac{1}{2}\ln\left(\frac{1-% \operatorname{dn}\left(x,k\right)}{1+\operatorname{dn}\left(x,k\right)}\right)% ,}}
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    DLMF:22.14.E14
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    cn ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E5.m2acdec
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    dn ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E6.m2addec
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    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2acdec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1amdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3amdec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aidec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C22.S1.XMD1.m1mdec
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