DLMF:23.6.E8 (Q7249)

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DLMF:23.6.E8
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    Statements

    Defining formula
    η 1 = - π 2 12 ⁢ ω 1 ⁢ θ 1 ′′′ ⁡ ( 0 , q ) θ 1 ′ ⁡ ( 0 , q ) . subscript 𝜂 1 superscript 𝜋 2 12 subscript 𝜔 1 diffop Jacobi-theta 1 3 0 𝑞 diffop Jacobi-theta 1 1 0 𝑞 {\displaystyle{\displaystyle\eta_{1}=-\frac{\pi^{2}}{12\omega_{1}}\frac{\theta% _{1}'''\left(0,q\right)}{\theta_{1}'\left(0,q\right)}.}}
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    DLMF id
    DLMF:23.6.E8
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    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.m2afdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    Q12066
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C23.S1.XMD10.m1gdec
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    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1gdec
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