DLMF:4.2.E6 (Q1502): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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.m2aadec
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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11219 / rank
 
Normal rank
Property / Symbols used: Q11219 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11219 / qualifier
 
xml-id: C4.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1fdec

Latest revision as of 18:01, 1 January 2020

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DLMF:4.2.E6
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    Statements

    Ln z = ln z + 2 k π i , multivalued-natural-logarithm 𝑧 𝑧 2 𝑘 𝜋 imaginary-unit {\displaystyle{\displaystyle\operatorname{Ln}z=\ln z+2k\pi\mathrm{i},}}
    0 references
    DLMF:4.2.E6
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2abdec
    0 references
    Ln z multivalued-natural-logarithm 𝑧 {\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}
    C4.S2.E1.m2aadec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2addec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C4.S1.XMD1.m1dec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1fdec
    0 references