DLMF:1.9.E22 (Q296): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2acdec
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.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q10818 / rank
 
Normal rank
Property / Symbols used: Q10818 / qualifier
 
Defining formula:

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

\Integers
Property / Symbols used: Q10818 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r20.m2aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1bdec
Property / Symbols used
 
Property / Symbols used: Q10814 / rank
 
Normal rank
Property / Symbols used: Q10814 / qualifier
 
Defining formula:

θ 𝜃 {\displaystyle{\displaystyle\theta}}

\theta
Property / Symbols used: Q10814 / qualifier
 
xml-id: C1.S9.XMD2.m1edec

Latest revision as of 16:07, 1 January 2020

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English
DLMF:1.9.E22
No description defined

    Statements

    Defining formula
    cos ⁡ n ⁢ θ + i ⁢ sin ⁡ n ⁢ θ = ( cos ⁡ θ + i ⁢ sin ⁡ θ ) n , 𝑛 𝜃 𝑖 𝑛 𝜃 superscript 𝜃 𝑖 𝜃 𝑛 {\displaystyle{\displaystyle\cos n\theta+i\sin n\theta=(\cos\theta+i\sin\theta% )^{n},}}
    0 references
    DLMF id
    DLMF:1.9.E22
    0 references
    constraint
    n ∈ ℤ 𝑛 {\displaystyle{\displaystyle n\in\mathbb{Z}}}
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    Q10818
    Defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2aadec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1bdec
    0 references
    Q10814
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C1.S9.XMD2.m1edec
    0 references
     
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