DLMF:1.16.E50 (Q658)

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DLMF:1.16.E50
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    Statements

    test
    ℱ ⁡ ( H ) = 1 2 ⁢ ℱ ⁡ ( 1 + sign ) = 1 2 ⁢ [ ℱ ⁡ ( 1 ) + ℱ ⁡ ( sign ) ] = π 2 ⁢ ( δ + i π ⁢ x ) , distributional-Fourier-transform Heaviside-H 1 2 distributional-Fourier-transform 1 sign 1 2 delimited-[] distributional-Fourier-transform 1 distributional-Fourier-transform sign 2 delta-distribution imaginary-unit 𝑥 {\displaystyle{\displaystyle\mathscr{F}\left(H\right)=\frac{1}{2}\mathscr{F}% \left(1+\operatorname{sign}\right)=\frac{1}{2}\left[\mathscr{F}\left(1\right)+% \mathscr{F}\left(\operatorname{sign}\right)\right]=\sqrt{\frac{\pi}{2}}\left(% \delta+\frac{\mathrm{i}}{\pi x}\right),}}
    0 references
    DLMF id
    DLMF:1.16.E50
    0 references
    Symbols used
    Heaviside function
    test
    H ⁡ ( x ) Heaviside-H 𝑥 {\displaystyle{\displaystyle H\left(\NVar{x}\right)}}
    xml-id
    C1.S16.E13.m2aidec
    0 references
     
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