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

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Property / constraint
 

z ( - , - 1 ] [ 1 , ) 𝑧 1 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,-1]\cup[1,\infty)}}

z\in\Complexes\setminus(-\infty,-1]\cup[1,\infty)
Property / constraint: z ( - , - 1 ] [ 1 , ) 𝑧 1 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,-1]\cup[1,\infty)}} / rank
 
Normal rank

Revision as of 17:03, 30 December 2019

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DLMF:4.37.E24
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    Statements

    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),}}
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    DLMF:4.37.E24
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    z ( - , - 1 ] [ 1 , ) 𝑧 1 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,-1]\cup[1,\infty)}}
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