DLMF:22.13.E15 (Q7066): 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:

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

\Jacobielldnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m2abdec

Revision as of 14:20, 2 January 2020

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DLMF:22.13.E15
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    Statements

    d 2 d z 2 dn ( z , k ) = ( 1 + k 2 ) dn ( z , k ) - 2 dn 3 ( z , k ) . derivative 𝑧 2 Jacobi-elliptic-dn 𝑧 𝑘 1 superscript superscript 𝑘 2 Jacobi-elliptic-dn 𝑧 𝑘 2 Jacobi-elliptic-dn 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{dn}\left(z,k\right)=(1+{k^{\prime}}^{2})\operatorname{dn}\left(z% ,k\right)-2{\operatorname{dn}^{3}}\left(z,k\right).}}
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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.m2abdec
    0 references