DLMF:1.17.E21 (Q680)

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DLMF:1.17.E21
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    Statements

    Defining formula
    δ ⁡ ( x - a ) = 1 2 ⁢ π ⁢ ∑ k = - ∞ ∞ e i ⁢ k ⁢ ( x - a ) . Dirac-delta 𝑥 𝑎 1 2 𝜋 superscript subscript 𝑘 superscript 𝑒 𝑖 𝑘 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{1}{2\pi}\sum_{k=-% \infty}^{\infty}e^{ik(x-a)}.}}
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    DLMF id
    DLMF:1.17.E21
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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.m2ahdec
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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.m2amdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
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