DLMF:36.4.E11 (Q9889): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12745 / rank
 
Normal rank
Property / Symbols used: Q12745 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q12745 / qualifier
 
xml-id: C36.S1.XMD10.m1edec
Property / Symbols used
 
Property / Symbols used: Q12746 / rank
 
Normal rank
Property / Symbols used: Q12746 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12746 / qualifier
 
xml-id: C36.S1.XMD11.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12741 / rank
 
Normal rank
Property / Symbols used: Q12741 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12741 / qualifier
 
xml-id: C36.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12748 / rank
 
Normal rank
Property / Symbols used: Q12748 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12748 / qualifier
 
xml-id: C36.S1.XMD9.m1fdec

Latest revision as of 15:08, 2 January 2020

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Language Label Description Also known as
English
DLMF:36.4.E11
No description defined

    Statements

    x + i y = - z 2 exp ( 2 3 i π m ) , 𝑥 𝑖 𝑦 superscript 𝑧 2 2 3 𝑖 𝜋 𝑚 {\displaystyle{\displaystyle x+iy=-z^{2}\exp\left(\tfrac{2}{3}i\pi m\right),}}
    0 references
    DLMF:36.4.E11
    0 references
    m = 0 , 1 , 2 𝑚 0 1 2 {\displaystyle{\displaystyle m=0,1,2}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2adec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C36.S1.XMD10.m1edec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C36.S1.XMD11.m1ddec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C36.S1.XMD2.m1dec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C36.S1.XMD9.m1fdec
    0 references