DLMF:4.8.E8 (Q1599): Difference between revisions

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

Ln ⁡ z multivalued-natural-logarithm 𝑧 {\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}

\Ln@@{\NVar{z}}
Property / Symbols used: general logarithm function / qualifier
 
xml-id: C4.S2.E1.m2acdec

Revision as of 18:11, 1 January 2020

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DLMF:4.8.E8
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    Statements

    Defining formula
    Ln ⁡ ( exp ⁡ z ) = z + 2 ⁢ k ⁢ π ⁢ i , multivalued-natural-logarithm 𝑧 𝑧 2 𝑘 𝜋 imaginary-unit {\displaystyle{\displaystyle\operatorname{Ln}\left(\exp z\right)=z+2k\pi% \mathrm{i},}}
    0 references
    DLMF id
    DLMF:4.8.E8
    0 references
    constraint
    k ∈ ℤ 𝑘 {\displaystyle{\displaystyle k\in\mathbb{Z}}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2abdec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10818
    Defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2abdec
    0 references
    general logarithm function
    Defining formula
    Ln ⁡ z multivalued-natural-logarithm 𝑧 {\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}
    xml-id
    C4.S2.E1.m2acdec
    0 references
     
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