DLMF:22.19.E9 (Q7183)

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DLMF:22.19.E9
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    Statements

    Defining formula
    x ⁢ ( t ) = a ⁢ cn ⁡ ( t ⁢ 2 ⁢ η - 1 , k ) , 𝑥 𝑡 𝑎 Jacobi-elliptic-cn 𝑡 2 𝜂 1 𝑘 {\displaystyle{\displaystyle x(t)=a\operatorname{cn}\left(t\sqrt{2\eta-1},k% \right),}}
    0 references
    DLMF id
    DLMF:22.19.E9
    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.m2aadec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1ddec
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    Q12038
    Defining formula
    x ⁢ ( t ) 𝑥 𝑡 {\displaystyle{\displaystyle x(t)}}
    xml-id
    C22.S19.XMD5.m1edec
    0 references
    Q12039
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C22.S19.XMD6.m1ddec
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    Q12041
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C22.S19.XMD8.m1cdec
    0 references
    Q12042
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C22.S19.XMD9.m1cdec
    0 references
     
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