DLMF:1.16.E27 (Q627): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec

Revision as of 16:36, 1 January 2020

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DLMF:1.16.E27
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    Statements

    Defining formula
    ⟨ D k ⁢ f , ϕ ⟩ = ( - 1 ) | k | ⁢ ∫ ℝ n f ⁢ ( x ) ⁢ ϕ ( k ) ⁢ ( x ) ⁢ d x , distribution superscript 𝐷 𝑘 𝑓 italic-ϕ superscript 1 𝑘 subscript 𝑛 𝑓 𝑥 superscript italic-ϕ 𝑘 𝑥 𝑥 {\displaystyle{\displaystyle\left\langle D^{k}f,\phi\right\rangle=(-1)^{\left|% k\right|}\int_{{\mathbb{R}^{n}}}f(x)\phi^{(k)}(x)\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:1.16.E27
    0 references
    constraint
    ϕ ∈ 𝒟 n italic-ϕ subscript 𝒟 𝑛 {\displaystyle{\displaystyle\phi\in\mathcal{D}_{n}}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10905
    Defining formula
    ⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    xml-id
    C1.S16.SS1.p5.m5aldec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
     
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