DLMF:1.16.E38 (Q646)

From testwiki
Revision as of 15:39, 1 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:1.16.E38
No description defined

    Statements

    test
    ⟨ ℱ ⁡ ( δ ) , ϕ ⟩ = ⟨ δ , ℱ ⁢ ( ϕ ) ⟩ = ⟨ δ , 1 2 ⁢ π ⁢ ∫ - ∞ ∞ ϕ ⁢ ( t ) ⁢ e i ⁢ x ⁢ t ⁢ d t ⟩ = 1 2 ⁢ π ⁢ ∫ - ∞ ∞ ϕ ⁢ ( t ) ⁢ d t = 1 2 ⁢ π ⁢ ⟨ 1 , ϕ ⟩ , distribution distributional-Fourier-transform delta-distribution italic-ϕ distribution delta-distribution ℱ italic-ϕ distribution delta-distribution 1 2 subscript superscript italic-ϕ 𝑡 imaginary-unit 𝑥 𝑡 𝑡 1 2 superscript subscript italic-ϕ 𝑡 𝑡 1 2 distribution 1 italic-ϕ {\displaystyle{\displaystyle\left\langle\mathscr{F}\left(\delta\right),\phi% \right\rangle=\left\langle\delta,\mathscr{F}(\phi)\right\rangle=\left\langle% \delta,\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}\phi(t){\mathrm{e}^{\mathrm% {i}xt}}\mathrm{d}t\right\rangle=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}% \phi(t)\mathrm{d}t=\frac{1}{\sqrt{2\pi}}\left\langle 1,\phi\right\rangle,}}
    0 references
    DLMF id
    DLMF:1.16.E38
    0 references
    constraint
    ϕ ∈ 𝒯 italic-ϕ 𝒯 {\displaystyle{\displaystyle\phi\in\mathcal{T}}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q646&oldid=3433"