1.16.E47 (Q625)

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1.16.E47
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    Statements

    DLMF defining formula
    ℱ ⁡ ( sign ′ ) = x i ⁢ ℱ ⁡ ( sign ) . distributional-Fourier-transform sign ′ 𝑥 imaginary-unit distributional-Fourier-transform sign {\displaystyle{\displaystyle\mathscr{F}\left({\operatorname{sign}^{\prime}}% \right)=\frac{x}{\mathrm{i}}\mathscr{F}\left(\operatorname{sign}\right).}}
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    Symbols used
    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.m2ahdec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
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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.m6acdec
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    Identifiers

     
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