DLMF:27.14.E13 (Q8112): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Euler’s reciprocal function / rank
 
Normal rank
Property / Symbols used: Euler’s reciprocal function / qualifier
 
test:

f ⁡ ( x ) Euler-phi 𝑥 {\displaystyle{\displaystyle\mathit{f}\left(\NVar{x}\right)}}

\EulerPhi@{\NVar{x}}
Property / Symbols used: Euler’s reciprocal function / qualifier
 
xml-id: C27.S14.E2.m2acdec

Revision as of 13:31, 2 January 2020

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DLMF:27.14.E13
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    Statements

    test
    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).}}
    0 references
    DLMF id
    DLMF:27.14.E13
    0 references
    constraint
    ℑ ⁡ τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}}
    0 references
    Symbols used
    Dedekind’s eta function (or Dedekind modular function)
    test
    η ⁡ ( τ ) Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}
    xml-id
    C27.S14.E12.m2aadec
    0 references
    Euler’s reciprocal function
    test
    f ⁡ ( x ) Euler-phi 𝑥 {\displaystyle{\displaystyle\mathit{f}\left(\NVar{x}\right)}}
    xml-id
    C27.S14.E2.m2acdec
    0 references
     
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