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

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Property / constraint
 

0 ≤ τ ≤ τ 0 0 𝜏 subscript 𝜏 0 {\displaystyle{\displaystyle 0\leq\tau\leq\tau_{0}}}

0\leq\tau\leq\tau_{0}
Property / constraint: 0 ≤ τ ≤ τ 0 0 𝜏 subscript 𝜏 0 {\displaystyle{\displaystyle 0\leq\tau\leq\tau_{0}}} / rank
 
Normal rank
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 14:40, 2 January 2020

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DLMF:10.20.E17
No description defined

    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}},}}
    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
    test
    coth ⁡ z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    xml-id
    C4.S28.E7.m2adec
    0 references
    hyperbolic tangent function
    test
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1mdec
    0 references
     
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