DLMF:22.8.E20 (Q6985)

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DLMF:22.8.E20
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    | 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,}}
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    DLMF:22.8.E20
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    cn ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E5.m2aidec
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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.m2aidec
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    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2aidec
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    det {\displaystyle{\displaystyle\det}}
    C1.S3.SS1.m1adec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1adec
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