DLMF:1.16.E41 (Q649)

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DLMF:1.16.E41
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    Statements

    test
    ⟨ ℱ ⁡ ( 1 ) , ϕ ⟩ = 2 ⁢ π ⁢ ⟨ ℱ ⁡ ( ℱ ⁡ ( δ ) ) , ϕ ⟩ = 2 ⁢ π ⁢ ⟨ ℱ ⁡ ( δ ) , ℱ ⁢ ( ϕ ) ⟩ = 2 ⁢ π ⁢ ⟨ δ , ℱ ⁢ ( ℱ ⁢ ( ϕ ) ) ⟩ = 2 ⁢ π ⁢ ⟨ δ , ϕ - ⟩ = 2 ⁢ π ⁢ ϕ ⁢ ( 0 ) , distribution distributional-Fourier-transform 1 italic-ϕ 2 distribution distributional-Fourier-transform distributional-Fourier-transform delta-distribution italic-ϕ 2 distribution distributional-Fourier-transform delta-distribution ℱ italic-ϕ 2 distribution delta-distribution ℱ ℱ italic-ϕ 2 distribution delta-distribution subscript italic-ϕ 2 italic-ϕ 0 {\displaystyle{\displaystyle\left\langle\mathscr{F}\left(1\right),\phi\right% \rangle=\sqrt{2\pi}\left\langle\mathscr{F}\left(\mathscr{F}\left(\delta\right)% \right),\phi\right\rangle=\sqrt{2\pi}\left\langle\mathscr{F}\left(\delta\right% ),\mathscr{F}(\phi)\right\rangle=\sqrt{2\pi}\left\langle\delta,\mathscr{F}(% \mathscr{F}(\phi))\right\rangle=\sqrt{2\pi}\left\langle\delta,\phi_{-}\right% \rangle=\sqrt{2\pi}\phi(0),}}
    0 references
    DLMF id
    DLMF:1.16.E41
    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.m2aedec
    0 references
     
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