DLMF:1.16.E49 (Q657)

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DLMF:1.16.E49
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    Statements

    test
    ⟨ ℱ ⁡ ( sign ) , ϕ ⟩ = i ⁢ 2 π ⁢ ⨍ - ∞ ∞ ϕ ⁢ ( x ) x ⁢ d x . distribution distributional-Fourier-transform sign italic-ϕ imaginary-unit 2 subscript superscript principal-value-integral italic-ϕ 𝑥 𝑥 𝑥 {\displaystyle{\displaystyle\left\langle\mathscr{F}\left(\operatorname{sign}% \right),\phi\right\rangle=\mathrm{i}\sqrt{\frac{2}{\pi}}\pvint^{\infty}_{-% \infty}\frac{\phi(x)}{x}\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:1.16.E49
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
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