DLMF:27.14.E14 (Q8113)

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DLMF:27.14.E14
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    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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    τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}}
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    η ( τ ) Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}
    C27.S14.E12.m2abdec
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    absent {\displaystyle{\displaystyle\Im}}
    C1.S9.E2.m2abdec
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