DLMF:4.37.E24 (Q1943): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11248 / rank
 
Normal rank
Property / Symbols used: Q11248 / qualifier
 
Defining formula:

arctanh ⁡ z hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}

\atanh@@{\NVar{z}}
Property / Symbols used: Q11248 / qualifier
 
xml-id: C4.S37.SS2.p1.m10acdec

Revision as of 19:17, 1 January 2020

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DLMF:4.37.E24
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    Statements

    Defining formula
    arctanh ⁡ z = 1 2 ⁢ ln ⁡ ( 1 + z 1 - z ) , hyperbolic-inverse-tangent 𝑧 1 2 1 𝑧 1 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}z=\tfrac{1}{2}\ln\left(\frac% {1+z}{1-z}\right),}}
    0 references
    DLMF id
    DLMF:4.37.E24
    0 references
    constraint
    z ∈ ℂ ∖ ( - ∞ , - 1 ] ∪ [ 1 , ∞ ) 𝑧 1 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,-1]\cup[1,\infty)}}
    0 references
    Symbols used
    Q11243
    Defining formula
    [ a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p2.t1.r1.m4aadec
    0 references
    Q10923
    Defining formula
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2acdec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2agdec
    0 references
    Q11248
    Defining formula
    arctanh ⁡ z hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m10acdec
    0 references
     
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