DLMF:22.6.E18 (Q6952): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11985 / rank
Normal rank
 
Property / Symbols used: Q11985 / qualifier
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
 
Property / Symbols used: Q11985 / qualifier
xml-id: C22.S1.XMD3.m1qdec
 
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
Normal rank
 
Property / Symbols used: Q11984 / qualifier
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
 
Property / Symbols used: Q11984 / qualifier
xml-id: C22.S1.XMD4.m1qdec
 

Latest revision as of 13:59, 2 January 2020

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DLMF:22.6.E18
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    Statements

    test
    1 - dn ⁡ ( 2 ⁢ z , k ) 1 + dn ⁡ ( 2 ⁢ z , k ) = k 2 ⁢ sn 2 ⁡ ( z , k ) ⁢ cn 2 ⁡ ( z , k ) dn 2 ⁡ ( z , k ) . 1 Jacobi-elliptic-dn 2 𝑧 𝑘 1 Jacobi-elliptic-dn 2 𝑧 𝑘 superscript 𝑘 2 Jacobi-elliptic-sn 2 𝑧 𝑘 Jacobi-elliptic-cn 2 𝑧 𝑘 Jacobi-elliptic-dn 2 𝑧 𝑘 {\displaystyle{\displaystyle\frac{1-\operatorname{dn}\left(2z,k\right)}{1+% \operatorname{dn}\left(2z,k\right)}=\frac{k^{2}{\operatorname{sn}^{2}}\left(z,% k\right){\operatorname{cn}^{2}}\left(z,k\right)}{{\operatorname{dn}^{2}}\left(% z,k\right)}.}}
    0 references
    DLMF id
    DLMF:22.6.E18
    0 references
    Symbols used
    Jacobian elliptic function
    test
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2aedec
    0 references
    Jacobian elliptic function
    test
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2aedec
    0 references
    Jacobian elliptic function
    test
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2aedec
    0 references
     
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