DLMF:23.15.E8 (Q7338)

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DLMF:23.15.E8
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    Statements

    Defining formula
    θ 1 ′ ⁡ ( 0 , q ) = ∂ ⁡ θ 1 ⁡ ( z , q ) / ∂ ⁡ z | z = 0 . diffop Jacobi-theta 1 1 0 𝑞 evaluated-at partial-derivative Jacobi-theta 1 𝑧 𝑞 𝑧 𝑧 0 {\displaystyle{\displaystyle\theta_{1}'\left(0,q\right)=\ifrac{\partial\theta_% {1}\left(z,q\right)}{\partial z}|_{z=0}.}}
    0 references
    DLMF id
    DLMF:23.15.E8
    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
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4adec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    Q12066
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C23.S1.XMD10.m1ddec
    0 references
    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1dec
    0 references
     
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