DLMF:1.14.E9 (Q501): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ahdec
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.m3agdec
Property / Symbols used
 
Property / Symbols used: Q10888 / rank
 
Normal rank
Property / Symbols used: Q10888 / qualifier
 
test:

F c ( x ) subscript 𝐹 𝑐 𝑥 {\displaystyle{\displaystyle F_{c}(x)}}

F_{c}(x)
Property / Symbols used: Q10888 / qualifier
 
xml-id: C1.S14.XMD4.m1dec

Latest revision as of 15:22, 1 January 2020

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DLMF:1.14.E9
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    Statements

    c ( f ) ( x ) = c f ( x ) = 2 π 0 f ( t ) cos ( x t ) d t , Fourier-cosine-transform 𝑓 𝑥 Fourier-cosine-transform 𝑓 𝑥 2 𝜋 subscript superscript 0 𝑓 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\mathscr{F}_{\mskip-3.0mu c}\left(f\right)\left(x% \right)=\mathscr{F}_{\mskip-3.0mu c}\mskip-1.0mu f\mskip 3.0mu \left(x\right)=% \sqrt{\frac{2}{\pi}}\int^{\infty}_{0}f(t)\cos\left(xt\right)\mathrm{d}t,}}
    0 references
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2afdec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1ahdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3agdec
    0 references
    F c ( x ) subscript 𝐹 𝑐 𝑥 {\displaystyle{\displaystyle F_{c}(x)}}
    C1.S14.XMD4.m1dec
    0 references