DLMF:10.20.E17 (Q3274)

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DLMF:10.20.E17
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    Statements

    test
    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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    DLMF id
    DLMF:10.20.E17
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    constraint
    0 ≤ τ ≤ τ 0 0 𝜏 subscript 𝜏 0 {\displaystyle{\displaystyle 0\leq\tau\leq\tau_{0}}}
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    Symbols used
    hyperbolic cotangent function
    test
    coth ⁡ z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    xml-id
    C4.S28.E7.m2adec
    0 references
     
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