DLMF:1.14.E1 (Q493): 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.m1adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
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.m2adec
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.m3adec

Latest revision as of 15:21, 1 January 2020

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DLMF:1.14.E1
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    Statements

    ( f ) ( x ) = f ( x ) = 1 2 π - f ( t ) e i x t d t . Fourier-transform 𝑓 𝑥 Fourier-transform 𝑓 𝑥 1 2 𝜋 subscript superscript 𝑓 𝑡 superscript 𝑒 𝑖 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\mathscr{F}\left(f\right)\left(x\right)=\mathscr{F% }\mskip-3.0mu f\mskip 3.0mu \left(x\right)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_% {-\infty}f(t)e^{ixt}\mathrm{d}t.}}
    0 references
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
    0 references