DLMF:1.16.E40 (Q648)

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DLMF:1.16.E40
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    Statements

    Defining formula
    ∫ - ∞ ∞ δ ⁡ ( t ) ⁢ e i ⁢ x ⁢ t ⁢ d t = 1 ; subscript superscript Dirac-delta 𝑡 imaginary-unit 𝑥 𝑡 𝑡 1 {\displaystyle{\displaystyle\int^{\infty}_{-\infty}\delta\left(t\right){% \mathrm{e}^{\mathrm{i}xt}}\mathrm{d}t=1;}}
    0 references
    DLMF id
    DLMF:1.16.E40
    0 references
    Symbols used
    Q10915
    Defining formula
    δ ⁡ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
    xml-id
    C1.S17.SS1.p1.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
     
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