DLMF:1.16.E26 (Q626): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10905 / rank
 
Normal rank
Property / Symbols used: Q10905 / qualifier
 
test:

⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}

\intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}
Property / Symbols used: Q10905 / qualifier
 
xml-id: C1.S16.SS1.p5.m5akdec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aadec
Property / Symbols used
 
Property / Symbols used: Q10812 / rank
 
Normal rank
Property / Symbols used: Q10812 / qualifier
 
test:

ℝ {\displaystyle{\displaystyle\mathbb{R}}}

\Reals
Property / Symbols used: Q10812 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r14.m2adec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1hdec
Property / Symbols used
 
Property / Symbols used: Q10911 / rank
 
Normal rank
Property / Symbols used: Q10911 / qualifier
 
test:

𝒟 n subscript 𝒟 𝑛 {\displaystyle{\displaystyle\mathcal{D}_{n}}}

\mathcal{D}_{n}
Property / Symbols used: Q10911 / qualifier
 
xml-id: C1.S16.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q10912 / rank
 
Normal rank
Property / Symbols used: Q10912 / qualifier
 
test:

ϕ ⁢ ( x 1 , x 2 , … , x n ) italic-ϕ subscript 𝑥 1 subscript 𝑥 2 … subscript 𝑥 𝑛 {\displaystyle{\displaystyle\phi(x_{1},x_{2},\dots,x_{n})}}

\phi(x_{1},x_{2},\dots,x_{n})
Property / Symbols used: Q10912 / qualifier
 
xml-id: C1.S16.XMD13.m1dec
Property / Symbols used
 
Property / Symbols used: Q10904 / rank
 
Normal rank
Property / Symbols used: Q10904 / qualifier
 
test:

Λ Λ {\displaystyle{\displaystyle\Lambda}}

\Lambda
Property / Symbols used: Q10904 / qualifier
 
xml-id: C1.S16.XMD4.m1jdec

Latest revision as of 15:36, 1 January 2020

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English
DLMF:1.16.E26
No description defined

    Statements

    test
    ⟨ Λ f , ϕ ⟩ = ∫ ℝ n f ⁢ ( x ) ⁢ ϕ ⁢ ( x ) ⁢ d x , distribution subscript Λ 𝑓 italic-ϕ subscript 𝑛 𝑓 𝑥 italic-ϕ 𝑥 𝑥 {\displaystyle{\displaystyle\left\langle\Lambda_{f},\phi\right\rangle=\int_{{% \mathbb{R}^{n}}}f(x)\phi(x)\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:1.16.E26
    0 references
    constraint
    ϕ ∈ 𝒟 n italic-ϕ subscript 𝒟 𝑛 {\displaystyle{\displaystyle\phi\in\mathcal{D}_{n}}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10905
    test
    ⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    xml-id
    C1.S16.SS1.p5.m5akdec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2addec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q10812
    test
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2adec
    0 references
    Q10757
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1hdec
    0 references
    Q10911
    test
    𝒟 n subscript 𝒟 𝑛 {\displaystyle{\displaystyle\mathcal{D}_{n}}}
    xml-id
    C1.S16.XMD10.m1dec
    0 references
    Q10912
    test
    ϕ ⁢ ( x 1 , x 2 , … , x n ) italic-ϕ subscript 𝑥 1 subscript 𝑥 2 … subscript 𝑥 𝑛 {\displaystyle{\displaystyle\phi(x_{1},x_{2},\dots,x_{n})}}
    xml-id
    C1.S16.XMD13.m1dec
    0 references
    Q10904
    test
    Λ Λ {\displaystyle{\displaystyle\Lambda}}
    xml-id
    C1.S16.XMD4.m1jdec
    0 references
     
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