Formula:599

Digital Library of Mathematical Functions ID 1.16.E29

${\displaystyle{\displaystyle\mathscr{F}(\phi)(\mathbf{x})=\mathscr{F}\phi(\mathbf{x})=\frac{1}{(2\pi)^{n/2}}\int_{{\mathbb{R}^{n}}}\phi(\mathbf{t})e^{i\mathbf{x}\cdot\mathbf{t}}\mathrm{d}\mathbf{t},}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\phi(x_{1},x_{2},\dots,x_{n})}}$: test function
 

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