DLMF:22.2.E6 (Q6928)

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DLMF:22.2.E6
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    Statements

    Defining formula
    dn ⁡ ( z , k ) = θ 4 ⁡ ( 0 , q ) θ 3 ⁡ ( 0 , q ) ⁢ θ 3 ⁡ ( ζ , q ) θ 4 ⁡ ( ζ , q ) = 1 nd ⁡ ( z , k ) , Jacobi-elliptic-dn 𝑧 𝑘 Jacobi-theta 4 0 𝑞 Jacobi-theta 3 0 𝑞 Jacobi-theta 3 𝜁 𝑞 Jacobi-theta 4 𝜁 𝑞 1 Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(z,k\right)=\frac{\theta_{4}% \left(0,q\right)}{\theta_{3}\left(0,q\right)}\frac{\theta_{3}\left(\zeta,q% \right)}{\theta_{4}\left(\zeta,q\right)}=\frac{1}{\operatorname{nd}\left(z,k% \right)},}}
    0 references
    DLMF id
    DLMF:22.2.E6
    0 references
    Symbols used
    Q11945
    Defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2acdec
    0 references
    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2addec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1cdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1edec
    0 references
    Q11986
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C22.S2.XMD2.m1cdec
    0 references
     
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