DLMF:10.20.E17 (Q3274)

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DLMF:10.20.E17
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    z = ± ( τ coth τ - τ 2 ) 1 2 ± i ( τ 2 - τ tanh τ ) 1 2 , 𝑧 plus-or-minus plus-or-minus superscript 𝜏 hyperbolic-cotangent 𝜏 superscript 𝜏 2 1 2 imaginary-unit superscript superscript 𝜏 2 𝜏 𝜏 1 2 {\displaystyle{\displaystyle z=\pm(\tau\coth\tau-\tau^{2})^{\frac{1}{2}}\pm% \mathrm{i}(\tau^{2}-\tau\tanh\tau)^{\frac{1}{2}},}}
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