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Formula:582

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Digital Library of Mathematical Functions ID 1.16.E12

⟨ 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}),}}


Constraint(s)

ϕ ∈ 𝒟 ⁢ ( I ) italic-ϕ 𝒟 𝐼 {\displaystyle{\displaystyle\phi\in\mathcal{D}(I)}}

Symbols List

  • δ x Dirac-delta-distribution 𝑥 {\displaystyle{\displaystyle\delta_{x}}} :
  • ⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}} :
  • ∈ {\displaystyle{\displaystyle\in}} :
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}} : test function
  • I 𝐼 {\displaystyle{\displaystyle I}} : interval
  • 𝒟 ⁢ ( I ) 𝒟 𝐼 {\displaystyle{\displaystyle\mathcal{D}(I)}} : test function space
  •  Edit this on Wikidata

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