DLMF:1.16.E29 (Q629): Difference between revisions

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Property / Symbols defined: Fourier transform of a test function (locally) / rank
 
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Revision as of 14:54, 30 December 2019

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DLMF:1.16.E29
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    ( ϕ ) ( 𝐱 ) = ϕ ( 𝐱 ) = 1 ( 2 π ) n / 2 n ϕ ( 𝐭 ) e i 𝐱 𝐭 d 𝐭 , italic-ϕ 𝐱 italic-ϕ 𝐱 1 superscript 2 𝜋 𝑛 2 subscript 𝑛 italic-ϕ 𝐭 superscript 𝑒 𝑖 𝐱 𝐭 𝐭 {\displaystyle{\displaystyle\mathscr{F}(\phi)(\mathbf{x})=\mathscr{F}\phi(% \mathbf{x})=\frac{1}{(2\pi)^{n/2}}\int_{{\mathbb{R}^{n}}}\phi(\mathbf{t})e^{i% \mathbf{x}\cdot\mathbf{t}}\mathrm{d}\mathbf{t},}}
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