DLMF:4.37.E25 (Q1944): Difference between revisions

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Property / constraint
 

x ( - , - 1 ) ( 1 , ) 𝑥 1 1 {\displaystyle{\displaystyle x\in(-\infty,-1)\cup(1,\infty)}}

x\in(-\infty,-1)\cup(1,\infty)
Property / constraint: x ( - , - 1 ) ( 1 , ) 𝑥 1 1 {\displaystyle{\displaystyle x\in(-\infty,-1)\cup(1,\infty)}} / rank
 
Normal rank

Revision as of 16:03, 30 December 2019

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DLMF:4.37.E25
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    Statements

    arctanh x = ± 1 2 π i + 1 2 ln ( x + 1 x - 1 ) , hyperbolic-inverse-tangent 𝑥 plus-or-minus 1 2 𝜋 𝑖 1 2 𝑥 1 𝑥 1 {\displaystyle{\displaystyle\operatorname{arctanh}x=\pm\tfrac{1}{2}\pi i+% \tfrac{1}{2}\ln\left(\frac{x+1}{x-1}\right),}}
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    x ( - , - 1 ) ( 1 , ) 𝑥 1 1 {\displaystyle{\displaystyle x\in(-\infty,-1)\cup(1,\infty)}}
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