DLMF:27.14.E14 (Q8113)

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DLMF:27.14.E14
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    Statements

    Defining formula
    η ⁡ ( a ⁢ τ + b c ⁢ τ + d ) = ε ⁢ ( - i ⁢ ( c ⁢ τ + d ) ) 1 2 ⁢ η ⁡ ( τ ) , Dedekind-modular-Eta 𝑎 𝜏 𝑏 𝑐 𝜏 𝑑 𝜀 superscript imaginary-unit 𝑐 𝜏 𝑑 1 2 Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\frac{a\tau+b}{c\tau+d}\right)=% \varepsilon(-\mathrm{i}(c\tau+d))^{\frac{1}{2}}\eta\left(\tau\right),}}
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    DLMF id
    DLMF:27.14.E14
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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.m2abdec
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    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2abdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    Q12267
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C27.S14.XMD4.m1dec
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    Q12268
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C27.S14.XMD5.m1dec
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    Q12269
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C27.S14.XMD6.m1dec
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    Q12270
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S14.XMD7.m1dec
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