DLMF:4.23.E27 (Q1779): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aidec

Revision as of 18:34, 1 January 2020

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DLMF:4.23.E27
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    Statements

    Defining formula
    arctan ⁡ ( i ⁢ y ) = ± 1 2 ⁢ π + i 2 ⁢ ln ⁡ ( y + 1 y - 1 ) , 𝑖 𝑦 plus-or-minus 1 2 𝜋 𝑖 2 𝑦 1 𝑦 1 {\displaystyle{\displaystyle\operatorname{arctan}\left(iy\right)=\pm\frac{1}{2% }\pi+\frac{i}{2}\ln\left(\frac{y+1}{y-1}\right),}}
    0 references
    DLMF id
    DLMF:4.23.E27
    0 references
    constraint
    y ∈ ( - ∞ , - 1 ) ∪ ( 1 , ∞ ) 𝑦 1 1 {\displaystyle{\displaystyle y\in(-\infty,-1)\cup(1,\infty)}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
     
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