Formula:467

Digital Library of Mathematical Functions ID 1.14.E6

${\displaystyle{\displaystyle(f*g)(t)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}F(x)G(x)e^{-itx}\mathrm{d}x,}}$

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
• ${\displaystyle{\displaystyle F(x)}}$: Fourier transform of f ( t )
• ${\displaystyle{\displaystyle*}}$: convolution (Fourier) (locally)
• ${\displaystyle{\displaystyle G(x)}}$: Fourier transform of g ( t )
 

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