DLMF:20.8.E1 (Q6830)

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DLMF:20.8.E1
No description defined

    Statements

    Defining formula
    θ 2 ⁡ ( 0 , q ) ⁢ θ 3 ⁡ ( z , q ) ⁢ θ 4 ⁡ ( z , q ) θ 2 ⁡ ( z , q ) = 2 ⁢ ∑ n = - ∞ ∞ ( - 1 ) n ⁢ q n 2 ⁢ e i ⁢ 2 ⁢ n ⁢ z q - n ⁢ e - i ⁢ z + q n ⁢ e i ⁢ z . Jacobi-theta 2 0 𝑞 Jacobi-theta 3 𝑧 𝑞 Jacobi-theta 4 𝑧 𝑞 Jacobi-theta 2 𝑧 𝑞 2 superscript subscript 𝑛 superscript 1 𝑛 superscript 𝑞 superscript 𝑛 2 superscript 𝑒 𝑖 2 𝑛 𝑧 superscript 𝑞 𝑛 superscript 𝑒 𝑖 𝑧 superscript 𝑞 𝑛 superscript 𝑒 𝑖 𝑧 {\displaystyle{\displaystyle\frac{\theta_{2}\left(0,q\right)\theta_{3}\left(z,% q\right)\theta_{4}\left(z,q\right)}{\theta_{2}\left(z,q\right)}=2\sum_{n=-% \infty}^{\infty}\frac{(-1)^{n}q^{n^{2}}e^{i2nz}}{q^{-n}e^{-iz}+q^{n}e^{iz}}.}}
    0 references
    DLMF id
    DLMF:20.8.E1
    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.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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