DLMF:18.28.E3 (Q5978)

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DLMF:18.28.E3
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    Statements

    test
    2 ⁢ π ⁢ sin ⁡ θ ⁢ w ⁢ ( cos ⁡ θ ) = | ( e 2 ⁢ i ⁢ θ ; q ) ∞ ( a ⁢ e i ⁢ θ , b ⁢ e i ⁢ θ , c ⁢ e i ⁢ θ , d ⁢ e i ⁢ θ ; q ) ∞ | 2 , 2 𝜋 𝜃 𝑤 𝜃 q-Pochhammer-symbol superscript 𝑒 2 𝑖 𝜃 𝑞 q-multiple-Pochhammer 𝑎 superscript 𝑒 𝑖 𝜃 𝑏 superscript 𝑒 𝑖 𝜃 𝑐 superscript 𝑒 𝑖 𝜃 𝑑 superscript 𝑒 𝑖 𝜃 𝑞 2 {\displaystyle{\displaystyle 2\pi\sin\theta\,w(\cos\theta)={\left|\frac{\left(% e^{2i\theta};q\right)_{\infty}}{\left(ae^{i\theta},be^{i\theta},ce^{i\theta},% de^{i\theta};q\right)_{\infty}}\right|^{2}},}}
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    DLMF id
    DLMF:18.28.E3
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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