DLMF:1.14.E44 (Q536)

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DLMF:1.14.E44
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    Statements

    test
    f ⁢ ( x ) = - 1 π ⁢ ⨍ - ∞ ∞ ℋ ⁡ f ⁡ ( u ) u - x ⁢ d u . 𝑓 𝑥 1 𝜋 subscript superscript principal-value-integral Hilbert-transform 𝑓 𝑢 𝑢 𝑥 𝑢 {\displaystyle{\displaystyle f(x)=-\frac{1}{\pi}\pvint^{\infty}_{-\infty}\frac% {\mathcal{H}\mskip-3.0mu f\mskip 3.0mu \left(u\right)}{u-x}\mathrm{d}u.}}
    0 references
    DLMF id
    DLMF:1.14.E44
    0 references
    Symbols used
    Q10895
    test
    ℋ ⁡ ( f ) ⁡ ( x ) Hilbert-transform 𝑓 𝑥 {\displaystyle{\displaystyle\mathcal{H}\left(\NVar{f}\right)\left(\NVar{x}% \right)}}
    xml-id
    C1.S14.SS5.p1.m2acdec
    0 references
     
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