DLMF:29.8.E1 (Q8704): 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
 
Defining formula:

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.m2adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

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

\Jacobiellsnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E4.m2adec
Property / Symbols used
 
Property / Symbols used: Q12369 / rank
 
Normal rank
Property / Symbols used: Q12369 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12369 / qualifier
 
xml-id: C29.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q12348 / rank
 
Normal rank
Property / Symbols used: Q12348 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12348 / qualifier
 
xml-id: C29.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q12350 / rank
 
Normal rank
Property / Symbols used: Q12350 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12350 / qualifier
 
xml-id: C29.S1.XMD8.m1dec

Latest revision as of 01:22, 2 January 2020

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DLMF:29.8.E1
No description defined

    Statements

    Defining formula
    x = k 2 ⁢ sn ⁡ ( z , k ) ⁢ sn ⁡ ( z 1 , k ) ⁢ sn ⁡ ( z 2 , k ) ⁢ sn ⁡ ( z 3 , k ) - k 2 k ′ 2 ⁢ cn ⁡ ( z , k ) ⁢ cn ⁡ ( z 1 , k ) ⁢ cn ⁡ ( z 2 , k ) ⁢ cn ⁡ ( z 3 , k ) + 1 k ′ 2 ⁢ dn ⁡ ( z , k ) ⁢ dn ⁡ ( z 1 , k ) ⁢ dn ⁡ ( z 2 , k ) ⁢ dn ⁡ ( z 3 , k ) , 𝑥 superscript 𝑘 2 Jacobi-elliptic-sn 𝑧 𝑘 Jacobi-elliptic-sn subscript 𝑧 1 𝑘 Jacobi-elliptic-sn subscript 𝑧 2 𝑘 Jacobi-elliptic-sn subscript 𝑧 3 𝑘 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-cn 𝑧 𝑘 Jacobi-elliptic-cn subscript 𝑧 1 𝑘 Jacobi-elliptic-cn subscript 𝑧 2 𝑘 Jacobi-elliptic-cn subscript 𝑧 3 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-dn 𝑧 𝑘 Jacobi-elliptic-dn subscript 𝑧 1 𝑘 Jacobi-elliptic-dn subscript 𝑧 2 𝑘 Jacobi-elliptic-dn subscript 𝑧 3 𝑘 {\displaystyle{\displaystyle x=k^{2}\operatorname{sn}\left(z,k\right)% \operatorname{sn}\left(z_{1},k\right)\operatorname{sn}\left(z_{2},k\right)% \operatorname{sn}\left(z_{3},k\right)-\frac{k^{2}}{{k^{\prime}}^{2}}% \operatorname{cn}\left(z,k\right)\operatorname{cn}\left(z_{1},k\right)% \operatorname{cn}\left(z_{2},k\right)\operatorname{cn}\left(z_{3},k\right)+% \frac{1}{{k^{\prime}}^{2}}\operatorname{dn}\left(z,k\right)\operatorname{dn}% \left(z_{1},k\right)\operatorname{dn}\left(z_{2},k\right)\operatorname{dn}% \left(z_{3},k\right),}}
    0 references
    DLMF id
    DLMF:29.8.E1
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2adec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2adec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2adec
    0 references
    Q12369
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C29.S1.XMD4.m1dec
    0 references
    Q12348
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1dec
    0 references
    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1dec
    0 references
     
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