DLMF:4.23.E26 (Q1778): Difference between revisions

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Property / constraint
 

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

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

Revision as of 17:01, 30 December 2019

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DLMF:4.23.E26
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    Statements

    arctan z = i 2 ln ( i + z i - z ) , 𝑧 𝑖 2 𝑖 𝑧 𝑖 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}z=\frac{i}{2}\ln\left(\frac{i% +z}{i-z}\right),}}
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    DLMF:4.23.E26
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    z / i ( - , - 1 ] [ 1 , ) 𝑧 𝑖 1 1 {\displaystyle{\displaystyle z/i\in\mathbb{C}\setminus(-\infty,-1]\cup[1,% \infty)}}
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