DLMF:1.14.E6 (Q498): Difference between revisions

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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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec
Property / Symbols used
 
Property / Symbols used: Q10886 / rank
 
Normal rank
Property / Symbols used: Q10886 / qualifier
 
test:

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

F(x)
Property / Symbols used: Q10886 / qualifier
 
xml-id: C1.S14.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: convolution (Fourier) (locally) / rank
 
Normal rank
Property / Symbols used: convolution (Fourier) (locally) / qualifier
 
test:

* {\displaystyle{\displaystyle*}}

*
Property / Symbols used: convolution (Fourier) (locally) / qualifier
 
xml-id: C1.S14.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q10887 / rank
 
Normal rank
Property / Symbols used: Q10887 / qualifier
 
test:

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

G(x)
Property / Symbols used: Q10887 / qualifier
 
xml-id: C1.S14.XMD3.m1dec

Latest revision as of 15:22, 1 January 2020

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English
DLMF:1.14.E6
No description defined

    Statements

    test
    ( f * g ) ⁢ ( t ) = 1 2 ⁢ π ⁢ ∫ - ∞ ∞ F ⁢ ( x ) ⁢ G ⁢ ( x ) ⁢ e - i ⁢ t ⁢ x ⁢ d x , 𝑓 𝑔 𝑡 1 2 𝜋 subscript superscript 𝐹 𝑥 𝐺 𝑥 superscript 𝑒 𝑖 𝑡 𝑥 𝑥 {\displaystyle{\displaystyle(f*g)(t)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}F(x)G(x)e^{-itx}\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:1.14.E6
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q10886
    test
    F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}
    xml-id
    C1.S14.XMD1.m1cdec
    0 references
    convolution (Fourier) (locally)
    test
    * {\displaystyle{\displaystyle*}}
    xml-id
    C1.S14.XMD2.m1adec
    0 references
    Q10887
    test
    G ⁢ ( x ) 𝐺 𝑥 {\displaystyle{\displaystyle G(x)}}
    xml-id
    C1.S14.XMD3.m1dec
    0 references
     
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