''Til 402:'' The function is defined by circ(''r'') = 1 0 ≤ ''r'' ≤ 1, and is 0 otherwise. The result is the amplitude distribution of the [[Airy disk]], and is expressed using ''J''<sub>1</sub> (the order 1 [[Bessel function]] of the first kind). {{harv|Stein|Weiss|1971|loc=Thm. IV.3.3}}
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=== Formler for generelle ''n''-dimensionelle funktioner ===
{| class="wikitable"
! !! Funktion !! Fouriertransformation <br /> unitær, ordinær frekvens !! Fouriertransformation <br /> unitær, angulær frekvens !! Fouriertransformation <br /> ikke-unitær, angulær frekvens
|-
|500
| style="text-align:center;"|<math>\displaystyle f(\mathbf x)\,</math>
| style="text-align:center;"|<math>\displaystyle \hat{f}(\boldsymbol \xi)=</math> <br />
<math>\displaystyle \int_{\mathbf{R}^n}f(\mathbf x) e^{-2\pi i \mathbf x \cdot \boldsymbol \xi }\, d^n \mathbf x </math>
| style="text-align:center;"|<math>\displaystyle \hat{f}(\boldsymbol \omega)=</math> <br />
<math>\displaystyle \frac{1}{{(2 \pi)}^{n/2}} \int_{\mathbf{R}^n} f(\mathbf x) e^{-i \boldsymbol \omega \cdot \mathbf x}\, d^n \mathbf x </math>
| style="text-align:center;"|<math>\displaystyle \hat{f}(\boldsymbol \nu)=</math> <br />
<math>\displaystyle \int_{\mathbf{R}^n}f(\mathbf x) e^{-i \mathbf x \cdot \boldsymbol \nu }\, d^n \mathbf x </math>
|-
|501
|<math>\displaystyle \chi_{[0,1]}(|\mathbf x|)(1-|\mathbf x|^2)^\delta</math>
| style="text-align:center;"|<math>\displaystyle \pi^{-\delta}\Gamma(\delta+1)|\boldsymbol \xi|^{-n/2-\delta}</math><br><math>\displaystyle \times J_{n/2+\delta}(2\pi|\boldsymbol \xi|)</math>
| style="text-align:center;"|<math>\displaystyle 2^{-\delta}\Gamma(\delta+1)\left|\boldsymbol \omega\right|^{-n/2-\delta}</math><br><math>\displaystyle \times J_{n/2+\delta}(|\boldsymbol \omega|)</math>
| style="text-align:center;"|<math>\displaystyle \pi^{-\delta}\Gamma(\delta+1)\left|\frac{\boldsymbol \nu}{2\pi}\right|^{-n/2-\delta}</math><br><math>\displaystyle \times J_{n/2+\delta}(|\boldsymbol \nu|)</math>
|-
|502
|<math>\displaystyle |\mathbf x|^{-\alpha}, \quad 0 < \operatorname{Re} \alpha < n.</math>
| style="text-align:center;"|<math>\displaystyle c_{n-\alpha, n}(2\pi)^{\alpha - n} |\boldsymbol \xi|^{-(n - \alpha)}</math>
| style="text-align:center;"|<math>\displaystyle c_{n-\alpha, n} (2\pi)^{-n/2}|\boldsymbol \omega|^{-(n - \alpha)}</math>
| style="text-align:center;"|<math>\displaystyle c_{n-\alpha, n} |\boldsymbol \nu|^{-(n - \alpha)}</math>
|-
|503
|<math>\displaystyle \frac{1}{\left\|\boldsymbol \sigma\right\|\left(2\pi\right)^{n/2}} e^{-\frac{1}{2} \mathbf x^{\mathrm T} \boldsymbol \sigma^{-\mathrm T} \boldsymbol \sigma^{-1} \mathbf x}</math>
| style="text-align:center;"|
| style="text-align:center;"|
| style="text-align:center;"|<math>\displaystyle e^{-\frac{1}{2} \boldsymbol \nu^{\mathrm T} \boldsymbol \sigma \boldsymbol \sigma^{\mathrm T} \boldsymbol \nu} </math>
|-
|504
|<math>\displaystyle e^{-2\pi\alpha|\mathbf x|}</math>
| style="text-align:center;"| <math>c_n\frac{\alpha}{(\alpha^2+|\xi|^2)^{(n+1)/2}}</math>
| style="text-align:center;"|
| style="text-align:center;"|
|}
Samfund Datalogi Videnskab Matematik