DLMF:10.20.E17 (Q3274)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.20.E17
No description defined

    Statements

    Defining formula
    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}},}}
    0 references
    DLMF id
    DLMF:10.20.E17
    0 references
    constraint
    0 ≤ τ ≤ τ 0 0 𝜏 subscript 𝜏 0 {\displaystyle{\displaystyle 0\leq\tau\leq\tau_{0}}}
    0 references
    Symbols used
    hyperbolic cotangent function
    Defining formula
    coth ⁡ z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    xml-id
    C4.S28.E7.m2adec
    0 references
    hyperbolic tangent function
    Defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1mdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3274&oldid=59897"