DLMF:1.15.E44 (Q586): 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
 
Defining formula:

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.m2akdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ardec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ajdec
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.m2akdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3ardec
Property / Symbols used
 
Property / Symbols used: Q10886 / rank
 
Normal rank
Property / Symbols used: Q10886 / qualifier
 
Defining formula:

F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}

F(x)
Property / Symbols used: Q10886 / qualifier
 
xml-id: C1.S14.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q10902 / rank
 
Normal rank
Property / Symbols used: Q10902 / qualifier
 
Defining formula:

σ R ⁢ ( θ ) subscript 𝜎 𝑅 𝜃 {\displaystyle{\displaystyle\sigma_{R}(\theta)}}

\sigma_{R}(\theta)
Property / Symbols used: Q10902 / qualifier
 
xml-id: C1.S15.XMD11.m1dec

Latest revision as of 16:32, 1 January 2020

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DLMF:1.15.E44
No description defined

    Statements

    Defining formula
    σ R ⁢ ( θ ) = 1 2 ⁢ π ⁢ ∫ - R R ( 1 - | t | R ) ⁢ e - i ⁢ θ ⁢ t ⁢ F ⁢ ( t ) ⁢ d t , subscript 𝜎 𝑅 𝜃 1 2 𝜋 subscript superscript 𝑅 𝑅 1 𝑡 𝑅 superscript 𝑒 𝑖 𝜃 𝑡 𝐹 𝑡 𝑡 {\displaystyle{\displaystyle\sigma_{R}(\theta)=\frac{1}{\sqrt{2\pi}}\int^{R}_{% -R}\left(1-\frac{|t|}{R}\right)e^{-i\theta t}F(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:1.15.E44
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ardec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2akdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ardec
    0 references
    Q10886
    Defining formula
    F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}
    xml-id
    C1.S14.XMD1.m1adec
    0 references
    Q10902
    Defining formula
    σ R ⁢ ( θ ) subscript 𝜎 𝑅 𝜃 {\displaystyle{\displaystyle\sigma_{R}(\theta)}}
    xml-id
    C1.S15.XMD11.m1dec
    0 references
     
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