DLMF:20.7.E25 (Q6820)

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DLMF:20.7.E25
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    Statements

    Defining formula
    d d z ⁡ ( θ 2 ⁡ ( z | τ ) θ 4 ⁡ ( z | τ ) ) = - θ 3 2 ⁡ ( 0 | τ ) ⁢ θ 1 ⁡ ( z | τ ) ⁢ θ 3 ⁡ ( z | τ ) θ 4 2 ⁡ ( z | τ ) . derivative 𝑧 Jacobi-theta-tau 2 𝑧 𝜏 Jacobi-theta-tau 4 𝑧 𝜏 Jacobi-theta-tau 3 2 0 𝜏 Jacobi-theta-tau 1 𝑧 𝜏 Jacobi-theta-tau 3 𝑧 𝜏 Jacobi-theta-tau 4 2 𝑧 𝜏 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\left(\frac{\theta_{% 2}\left(z\middle|\tau\right)}{\theta_{4}\left(z\middle|\tau\right)}\right)=-% \frac{{\theta_{3}^{2}}\left(0\middle|\tau\right)\theta_{1}\left(z\middle|\tau% \right)\theta_{3}\left(z\middle|\tau\right)}{{\theta_{4}^{2}}\left(z\middle|% \tau\right)}.}}
    0 references
    DLMF id
    DLMF:20.7.E25
    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.m1ajdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1udec
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    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1jdec
    0 references
     
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