1.16.E48 (Q626)

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1.16.E48
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    Statements

    DLMF defining formula
    ℱ ⁡ ( sign ) = 2 π ⁢ i x , distributional-Fourier-transform sign 2 imaginary-unit 𝑥 {\displaystyle{\displaystyle\mathscr{F}\left(\operatorname{sign}\right)=\sqrt{% \frac{2}{\pi}}\,\frac{\mathrm{i}}{x},}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
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    Fourier transform of a tempered distribution
    DLMF defining formula
    ℱ ⁡ ( u ) distributional-Fourier-transform 𝑢 {\displaystyle{\displaystyle\mathscr{F}\left(\NVar{u}\right)}}
    xml-id
    C1.S16.E35.m2aidec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aidec
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    Q10871
    DLMF defining formula
    sign ⁡ x sign 𝑥 {\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}
    xml-id
    introduction.Sx4.p2.t1.r18.m6addec
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    Identifiers

     
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