DLMF:22.2.E11 (Q6933)

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DLMF:22.2.E11
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    Statements

    Defining formula
    p ⁣ q ⁡ ( z , k ) = θ p ⁡ ( z | τ ) / θ q ⁡ ( z | τ ) , abstract-Jacobi-elliptic p q 𝑧 𝑘 Jacobi-theta-tau 𝑝 𝑧 𝜏 Jacobi-theta-tau 𝑞 𝑧 𝜏 {\displaystyle{\displaystyle\operatorname{pq}\left(z,k\right)=\ifrac{\theta_{p% }\left(z\middle|\tau\right)}{\theta_{q}\left(z\middle|\tau\right)},}}
    0 references
    DLMF id
    DLMF:22.2.E11
    0 references
    Symbols used
    Q11946
    Defining formula
    θ j ⁡ ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    xml-id
    C20.S2.SS1.m1adec
    0 references
    generic Jacobian elliptic function
    Defining formula
    p ⁣ q ⁡ ( z , k ) abstract-Jacobi-elliptic p q 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{pq}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E10.m2aadec
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    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2ahdec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1hdec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1jdec
    0 references
    Q11987
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C22.S1.XMD6.m1dec
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