DLMF:27.14.E12 (Q8111)

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DLMF:27.14.E12
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    Statements

    Defining formula
    η ⁡ ( τ ) = e π ⁢ i ⁢ τ / 12 ⁢ ∏ n = 1 ∞ ( 1 - e 2 ⁢ π ⁢ i ⁢ n ⁢ τ ) , Dedekind-modular-Eta 𝜏 superscript 𝑒 imaginary-unit 𝜏 12 superscript subscript product 𝑛 1 1 superscript 𝑒 2 imaginary-unit 𝑛 𝜏 {\displaystyle{\displaystyle\eta\left(\tau\right)=e^{\pi\mathrm{i}\tau/12}% \prod_{n=1}^{\infty}(1-e^{2\pi\mathrm{i}n\tau}),}}
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    DLMF id
    DLMF:27.14.E12
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    constraint
    ℑ ⁡ τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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