DLMF:10.20.E17 (Q3274): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: hyperbolic cotangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic cotangent function / qualifier
 
test:

coth z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}

\coth@@{\NVar{z}}
Property / Symbols used: hyperbolic cotangent function / qualifier
 
xml-id: C4.S28.E7.m2adec
Property / Symbols used
 
Property / Symbols used: hyperbolic tangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic tangent function / qualifier
 
test:

tanh z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}

\tanh@@{\NVar{z}}
Property / Symbols used: hyperbolic tangent function / qualifier
 
xml-id: C4.S28.E4.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2addec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1mdec

Latest revision as of 15:40, 2 January 2020

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DLMF:10.20.E17
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    Statements

    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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    0 τ τ 0 0 𝜏 subscript 𝜏 0 {\displaystyle{\displaystyle 0\leq\tau\leq\tau_{0}}}
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    coth z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    C4.S28.E7.m2adec
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    tanh z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    C4.S28.E4.m2adec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2addec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1mdec
    0 references