DLMF:1.16.E46 (Q654)

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DLMF:1.16.E46
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    Statements

    Defining formula
    ℱ ⁡ ( sign ′ ) = ℱ ⁡ ( 2 ⁢ H ′ ) = 2 ⁢ ℱ ⁡ ( δ ) = 2 π , distributional-Fourier-transform sign ′ distributional-Fourier-transform 2 diffop Heaviside-H 1 2 distributional-Fourier-transform delta-distribution 2 {\displaystyle{\displaystyle\mathscr{F}\left({\operatorname{sign}^{\prime}}% \right)=\mathscr{F}\left(2H'\right)=2\mathscr{F}\left(\delta\right)=\sqrt{% \frac{2}{\pi}},}}
    0 references
    DLMF id
    DLMF:1.16.E46
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    Symbols used
    Heaviside function
    Defining formula
    H ⁡ ( x ) Heaviside-H 𝑥 {\displaystyle{\displaystyle H\left(\NVar{x}\right)}}
    xml-id
    C1.S16.E13.m2ahdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
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    Q10908
    Defining formula
    δ x Dirac-delta-distribution 𝑥 {\displaystyle{\displaystyle\delta_{x}}}
    xml-id
    C1.S16.SS3.m1akdec
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    Fourier transform of a tempered distribution
    Defining formula
    ℱ ⁡ ( u ) distributional-Fourier-transform 𝑢 {\displaystyle{\displaystyle\mathscr{F}\left(\NVar{u}\right)}}
    xml-id
    C1.S16.E35.m2agdec
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