DLMF:22.8.E23 (Q6988): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1cdec

Latest revision as of 15:05, 2 January 2020

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DLMF:22.8.E23
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    Statements

    Defining formula
    | sn ⁡ z 1 ⁢ cn ⁡ z 1 cn ⁡ z 1 ⁢ dn ⁡ z 1 cn ⁡ z 1 dn ⁡ z 1 sn ⁡ z 2 ⁢ cn ⁡ z 2 cn ⁡ z 2 ⁢ dn ⁡ z 2 cn ⁡ z 2 dn ⁡ z 2 sn ⁡ z 3 ⁢ cn ⁡ z 3 cn ⁡ z 3 ⁢ dn ⁡ z 3 cn ⁡ z 3 dn ⁡ z 3 sn ⁡ z 4 ⁢ cn ⁡ z 4 cn ⁡ z 4 ⁢ dn ⁡ z 4 cn ⁡ z 4 dn ⁡ z 4 | = 0 . Jacobi-elliptic-sn subscript 𝑧 1 𝑘 Jacobi-elliptic-cn subscript 𝑧 1 𝑘 Jacobi-elliptic-cn subscript 𝑧 1 𝑘 Jacobi-elliptic-dn subscript 𝑧 1 𝑘 Jacobi-elliptic-cn subscript 𝑧 1 𝑘 Jacobi-elliptic-dn subscript 𝑧 1 𝑘 Jacobi-elliptic-sn subscript 𝑧 2 𝑘 Jacobi-elliptic-cn subscript 𝑧 2 𝑘 Jacobi-elliptic-cn subscript 𝑧 2 𝑘 Jacobi-elliptic-dn subscript 𝑧 2 𝑘 Jacobi-elliptic-cn subscript 𝑧 2 𝑘 Jacobi-elliptic-dn subscript 𝑧 2 𝑘 Jacobi-elliptic-sn subscript 𝑧 3 𝑘 Jacobi-elliptic-cn subscript 𝑧 3 𝑘 Jacobi-elliptic-cn subscript 𝑧 3 𝑘 Jacobi-elliptic-dn subscript 𝑧 3 𝑘 Jacobi-elliptic-cn subscript 𝑧 3 𝑘 Jacobi-elliptic-dn subscript 𝑧 3 𝑘 Jacobi-elliptic-sn subscript 𝑧 4 𝑘 Jacobi-elliptic-cn subscript 𝑧 4 𝑘 Jacobi-elliptic-cn subscript 𝑧 4 𝑘 Jacobi-elliptic-dn subscript 𝑧 4 𝑘 Jacobi-elliptic-cn subscript 𝑧 4 𝑘 Jacobi-elliptic-dn subscript 𝑧 4 𝑘 0 {\displaystyle{\displaystyle\begin{vmatrix}\operatorname{sn}z_{1}\operatorname% {cn}z_{1}&\operatorname{cn}z_{1}\operatorname{dn}z_{1}&\operatorname{cn}z_{1}&% \operatorname{dn}z_{1}\\ \operatorname{sn}z_{2}\operatorname{cn}z_{2}&\operatorname{cn}z_{2}% \operatorname{dn}z_{2}&\operatorname{cn}z_{2}&\operatorname{dn}z_{2}\\ \operatorname{sn}z_{3}\operatorname{cn}z_{3}&\operatorname{cn}z_{3}% \operatorname{dn}z_{3}&\operatorname{cn}z_{3}&\operatorname{dn}z_{3}\\ \operatorname{sn}z_{4}\operatorname{cn}z_{4}&\operatorname{cn}z_{4}% \operatorname{dn}z_{4}&\operatorname{cn}z_{4}&\operatorname{dn}z_{4}\end{% vmatrix}=0.}}
    0 references
    DLMF id
    DLMF:22.8.E23
    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.m2akdec
    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.m2akdec
    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.m2akdec
    0 references
    Q10765
    Defining formula
    det {\displaystyle{\displaystyle\det}}
    xml-id
    C1.S3.SS1.m1aadec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1ddec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1cdec
    0 references
     
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