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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10923 / rank
 
Normal rank
Property / Symbols used: Q10923 / qualifier
 
Defining formula:

ℂ {\displaystyle{\displaystyle\mathbb{C}}}

\Complexes
Property / Symbols used: Q10923 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r1.m2acdec

Revision as of 18:33, 1 January 2020

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DLMF:4.23.E26
No description defined

    Statements

    Defining formula
    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),}}
    0 references
    DLMF id
    DLMF:4.23.E26
    0 references
    constraint
    z / i ∈ ℂ ∖ ( - ∞ , - 1 ] ∪ [ 1 , ∞ ) 𝑧 𝑖 1 1 {\displaystyle{\displaystyle z/i\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.m4abdec
    0 references
    Q10923
    Defining formula
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2acdec
    0 references
     
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