DLMF:4.2.E7 (Q1503): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aedec

Revision as of 18:01, 1 January 2020

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DLMF:4.2.E7
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    Statements

    Defining formula
    ln ⁡ ( x ± i ⁢ 0 ) = ln ⁡ | x | ± i ⁢ π , plus-or-minus 𝑥 imaginary-unit 0 plus-or-minus 𝑥 𝑖 𝜋 {\displaystyle{\displaystyle\ln\left(x\pm\mathrm{i}0\right)=\ln|x|\pm i\pi,}}
    0 references
    DLMF id
    DLMF:4.2.E7
    0 references
    constraint
    - ∞ < x < 0 𝑥 0 {\displaystyle{\displaystyle-\infty<x<0}}
    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.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aedec
    0 references
     
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