DLMF:1.16.E10 (Q610): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10908 / rank
 
Normal rank
Property / Symbols used: Q10908 / qualifier
 
Defining formula:

δ x Dirac-delta-distribution 𝑥 {\displaystyle{\displaystyle\delta_{x}}}

\deltaDistribution[x]
Property / Symbols used: Q10908 / qualifier
 
xml-id: C1.S16.SS3.m1adec
Property / Symbols used
 
Property / Symbols used: Q10905 / rank
 
Normal rank
Property / Symbols used: Q10905 / qualifier
 
Defining formula:

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.m5agdec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10903 / rank
 
Normal rank
Property / Symbols used: Q10903 / qualifier
 
Defining formula:

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

\phi(x)
Property / Symbols used: Q10903 / qualifier
 
xml-id: C1.S16.XMD1.m1idec
Property / Symbols used
 
Property / Symbols used: Q10906 / rank
 
Normal rank
Property / Symbols used: Q10906 / qualifier
 
Defining formula:

I 𝐼 {\displaystyle{\displaystyle I}}

I
Property / Symbols used: Q10906 / qualifier
 
xml-id: C1.S16.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q10907 / rank
 
Normal rank
Property / Symbols used: Q10907 / qualifier
 
Defining formula:

𝒟 ( I ) 𝒟 𝐼 {\displaystyle{\displaystyle\mathcal{D}(I)}}

\mathcal{D}(I)
Property / Symbols used: Q10907 / qualifier
 
xml-id: C1.S16.XMD3.m1adec

Latest revision as of 16:35, 1 January 2020

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DLMF:1.16.E10
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    Statements

    δ , ϕ = ϕ ( 0 ) , distribution delta-distribution italic-ϕ italic-ϕ 0 {\displaystyle{\displaystyle\left\langle\delta,\phi\right\rangle=\phi(0),}}
    0 references
    DLMF:1.16.E10
    0 references
    ϕ 𝒟 ( I ) italic-ϕ 𝒟 𝐼 {\displaystyle{\displaystyle\phi\in\mathcal{D}(I)}}
    0 references
    δ x Dirac-delta-distribution 𝑥 {\displaystyle{\displaystyle\delta_{x}}}
    C1.S16.SS3.m1adec
    0 references
    Λ , ϕ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    C1.S16.SS1.p5.m5agdec
    0 references
    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    ϕ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    C1.S16.XMD1.m1idec
    0 references
    I 𝐼 {\displaystyle{\displaystyle I}}
    C1.S16.XMD2.m1bdec
    0 references
    𝒟 ( I ) 𝒟 𝐼 {\displaystyle{\displaystyle\mathcal{D}(I)}}
    C1.S16.XMD3.m1adec
    0 references