DLMF:1.17.E2 (Q661)

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DLMF:1.17.E2
No description defined

    Statements

    Defining formula
    ∫ - ∞ ∞ δ ⁡ ( x - a ) ⁢ ϕ ⁢ ( x ) ⁢ d x = ϕ ⁢ ( a ) , superscript subscript Dirac-delta 𝑥 𝑎 italic-ϕ 𝑥 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\delta\left(x-a\right)\phi(% x)\mathrm{d}x=\phi(a),}}
    0 references
    DLMF id
    DLMF:1.17.E2
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    constraint
    a ∈ ℝ 𝑎 {\displaystyle{\displaystyle a\in\mathbb{R}}}
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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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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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    Q10812
    Defining formula
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2aadec
    0 references
    Q10916
    Defining formula
    ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    xml-id
    C1.S17.XMD1.m1dec
    0 references
     
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