DLMF:1.16.E12 (Q612): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1bdec
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.m1kdec
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.m1ddec
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.m1cdec

Latest revision as of 16:35, 1 January 2020

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DLMF:1.16.E12
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    Statements

    δ x 0 ( n ) , ϕ = ( - 1 ) n ϕ ( n ) ( x 0 ) , distribution Dirac-delta-distribution subscript 𝑥 0 𝑛 italic-ϕ superscript 1 𝑛 superscript italic-ϕ 𝑛 subscript 𝑥 0 {\displaystyle{\displaystyle\left\langle{\delta_{x_{0}}^{(n)}},\phi\right% \rangle=(-1)^{n}\phi^{(n)}(x_{0}),}}
    0 references
    DLMF:1.16.E12
    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.m1abdec
    0 references
    Λ , ϕ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    C1.S16.SS1.p5.m5aidec
    0 references
    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2acdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C1.S1.XMD7.m1bdec
    0 references
    ϕ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    C1.S16.XMD1.m1kdec
    0 references
    I 𝐼 {\displaystyle{\displaystyle I}}
    C1.S16.XMD2.m1ddec
    0 references
    𝒟 ( I ) 𝒟 𝐼 {\displaystyle{\displaystyle\mathcal{D}(I)}}
    C1.S16.XMD3.m1cdec
    0 references