DLMF:22.6.E1 (Q6935)

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DLMF:22.6.E1
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    Statements

    Defining formula
    sn 2 ⁡ ( z , k ) + cn 2 ⁡ ( z , k ) = k 2 ⁢ sn 2 ⁡ ( z , k ) + dn 2 ⁡ ( z , k ) = 1 , Jacobi-elliptic-sn 2 𝑧 𝑘 Jacobi-elliptic-cn 2 𝑧 𝑘 superscript 𝑘 2 Jacobi-elliptic-sn 2 𝑧 𝑘 Jacobi-elliptic-dn 2 𝑧 𝑘 1 {\displaystyle{\displaystyle{\operatorname{sn}^{2}}\left(z,k\right)+{% \operatorname{cn}^{2}}\left(z,k\right)=k^{2}{\operatorname{sn}^{2}}\left(z,k% \right)+{\operatorname{dn}^{2}}\left(z,k\right)=1,}}
    0 references
    DLMF id
    DLMF:22.6.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
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1dec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1dec
    0 references
     
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