DLMF:1.16.E43 (Q651)

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DLMF:1.16.E43
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    Statements

    Defining formula
    1 2 ⁢ π ⁢ ∫ - ∞ ∞ e i ⁢ x ⁢ t ⁢ d t = δ ⁡ ( x ) ; 1 2 subscript superscript imaginary-unit 𝑥 𝑡 𝑡 Dirac-delta 𝑥 {\displaystyle{\displaystyle\frac{1}{2\pi}\int^{\infty}_{-\infty}{\mathrm{e}^{% \mathrm{i}xt}}\mathrm{d}t=\delta\left(x\right);}}
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    DLMF id
    DLMF:1.16.E43
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    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.m2aadec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2agdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
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