DLMF:4.4.E7 (Q1541): Difference between revisions

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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.m2addec
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: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2acdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2addec
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

Latest revision as of 17:05, 1 January 2020

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DLMF:4.4.E7
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    Statements

    e 2 π k i = 1 , superscript 𝑒 2 𝜋 𝑘 imaginary-unit 1 {\displaystyle{\displaystyle e^{2\pi k\mathrm{i}}=1,}}
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    k 𝑘 {\displaystyle{\displaystyle k\in\mathbb{Z}}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
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    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2addec
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    {\displaystyle{\displaystyle\mathbb{Z}}}
    introduction.Sx4.p2.t1.r20.m2adec
    0 references