DLMF:27.14.E13 (Q8112)

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DLMF:27.14.E13
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    Statements

    Defining formula
    η ⁡ ( τ ) = e π ⁢ i ⁢ τ / 12 ⁢ f ⁡ ( e 2 ⁢ π ⁢ i ⁢ τ ) . Dedekind-modular-Eta 𝜏 superscript 𝑒 imaginary-unit 𝜏 12 Euler-phi superscript 𝑒 2 imaginary-unit 𝜏 {\displaystyle{\displaystyle\eta\left(\tau\right)=e^{\pi\mathrm{i}\tau/12}% \mathit{f}\left(e^{2\pi\mathrm{i}\tau}\right).}}
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    DLMF id
    DLMF:27.14.E13
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    constraint
    ℑ ⁡ τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}}
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    Symbols used
    Dedekind’s eta function (or Dedekind modular function)
    Defining formula
    η ⁡ ( τ ) Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}
    xml-id
    C27.S14.E12.m2aadec
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    Euler’s reciprocal function
    Defining formula
    f ⁡ ( x ) Euler-phi 𝑥 {\displaystyle{\displaystyle\mathit{f}\left(\NVar{x}\right)}}
    xml-id
    C27.S14.E2.m2acdec
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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.m2acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
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