DLMF:4.2.E23 (Q1519): Difference between revisions

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Property / constraint
 

k 𝑘 {\displaystyle{\displaystyle k\in\mathbb{Z}}}

k\in\Integers
Property / constraint: k 𝑘 {\displaystyle{\displaystyle k\in\mathbb{Z}}} / rank
 
Normal rank
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
 
test:

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.m2aedec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

{\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec
Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
test:

exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2addec
Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Im}}

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q10818 / rank
 
Normal rank
Property / Symbols used: Q10818 / qualifier
 
test:

{\displaystyle{\displaystyle\mathbb{Z}}}

\Integers
Property / Symbols used: Q10818 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r20.m2adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11219 / rank
 
Normal rank
Property / Symbols used: Q11219 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11219 / qualifier
 
xml-id: C4.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1pdec

Latest revision as of 17:03, 1 January 2020

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DLMF:4.2.E23
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    Statements

    ph ( exp z ) = z + 2 k π , phase 𝑧 𝑧 2 𝑘 𝜋 {\displaystyle{\displaystyle\operatorname{ph}\left(\exp z\right)=\Im z+2k\pi,}}
    0 references
    0 references
    k 𝑘 {\displaystyle{\displaystyle k\in\mathbb{Z}}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
    0 references
    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2addec
    0 references
    absent {\displaystyle{\displaystyle\Im}}
    C1.S9.E2.m2adec
    0 references
    {\displaystyle{\displaystyle\mathbb{Z}}}
    introduction.Sx4.p2.t1.r20.m2adec
    0 references
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1abdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C4.S1.XMD1.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1pdec
    0 references