DLMF:22.8.E20 (Q6985): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
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.m1dec

Latest revision as of 15:05, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.8.E20
No description defined

    Statements

    | sn z 1 cn z 1 dn z 1 1 sn z 2 cn z 2 dn z 2 1 sn z 3 cn z 3 dn z 3 1 sn z 4 cn z 4 dn z 4 1 | = 0 , Jacobi-elliptic-sn subscript 𝑧 1 𝑘 Jacobi-elliptic-cn subscript 𝑧 1 𝑘 Jacobi-elliptic-dn subscript 𝑧 1 𝑘 1 Jacobi-elliptic-sn subscript 𝑧 2 𝑘 Jacobi-elliptic-cn subscript 𝑧 2 𝑘 Jacobi-elliptic-dn subscript 𝑧 2 𝑘 1 Jacobi-elliptic-sn subscript 𝑧 3 𝑘 Jacobi-elliptic-cn subscript 𝑧 3 𝑘 Jacobi-elliptic-dn subscript 𝑧 3 𝑘 1 Jacobi-elliptic-sn subscript 𝑧 4 𝑘 Jacobi-elliptic-cn subscript 𝑧 4 𝑘 Jacobi-elliptic-dn subscript 𝑧 4 𝑘 1 0 {\displaystyle{\displaystyle\begin{vmatrix}\operatorname{sn}z_{1}&% \operatorname{cn}z_{1}&\operatorname{dn}z_{1}&1\\ \operatorname{sn}z_{2}&\operatorname{cn}z_{2}&\operatorname{dn}z_{2}&1\\ \operatorname{sn}z_{3}&\operatorname{cn}z_{3}&\operatorname{dn}z_{3}&1\\ \operatorname{sn}z_{4}&\operatorname{cn}z_{4}&\operatorname{dn}z_{4}&1\end{% vmatrix}=0,}}
    0 references
    DLMF:22.8.E20
    0 references
    cn ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E5.m2aidec
    0 references
    dn ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E6.m2aidec
    0 references
    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2aidec
    0 references
    det {\displaystyle{\displaystyle\det}}
    C1.S3.SS1.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1dec
    0 references