DLMF:1.17.E3 (Q662): Difference between revisions

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‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q10916 / rank
 
Normal rank
Property / Symbols used: Q10916 / qualifier
 
Defining formula:

ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}

\phi(x)
Property / Symbols used: Q10916 / qualifier
 
xml-id: C1.S17.XMD1.m1adec

Latest revision as of 16:42, 1 January 2020

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DLMF:1.17.E3
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    Statements

    Defining formula
    lim n → ∞ ⁡ ∫ - ∞ ∞ δ n ⁡ ( x - a ) ⁢ ϕ ⁢ ( x ) ⁢ d x = ϕ ⁢ ( a ) , subscript → 𝑛 superscript subscript Dirac-delta-sequence 𝑛 𝑥 𝑎 italic-ϕ 𝑥 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\lim_{n\to\infty}\int_{-\infty}^{\infty}\delta_{n}% \left(x-a\right)\phi(x)\mathrm{d}x=\phi(a),}}
    0 references
    DLMF id
    DLMF:1.17.E3
    0 references
    Symbols used
    Q10917
    Defining formula
    δ n ⁡ ( x ) Dirac-delta-sequence 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}\left(\NVar{x}\right)}}
    xml-id
    C1.S17.SS1.p1.m6adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1dec
    0 references
    Q10916
    Defining formula
    ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    xml-id
    C1.S17.XMD1.m1adec
    0 references
     
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