DLMF:1.16.E48 (Q656)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:1.16.E48
No description defined

    Statements

    Defining formula
    ℱ ⁡ ( sign ) = 2 π ⁢ i x , distributional-Fourier-transform sign 2 imaginary-unit 𝑥 {\displaystyle{\displaystyle\mathscr{F}\left(\operatorname{sign}\right)=\sqrt{% \frac{2}{\pi}}\,\frac{\mathrm{i}}{x},}}
    0 references
    DLMF id
    DLMF:1.16.E48
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    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.m2aidec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aidec
    0 references
    Q10897
    Defining formula
    sign ⁡ x sign 𝑥 {\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}
    xml-id
    introduction.Sx4.p2.t1.r18.m6addec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q656&oldid=23795"