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1.16#Ex5
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Formula:609
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MaRDI QID
Q609
Label: 1.16#Ex5
Digital Library of Mathematical Functions ID
1.16#Ex5
1
(
2
π
)
n
/
2
∫
ℝ
n
P
(
𝐭
)
ϕ
(
𝐭
)
e
i
𝐱
⋅
𝐭
d
𝐭
=
P
(
D
)
F
(
𝐱
)
.
1
superscript
2
𝜋
𝑛
2
subscript
𝑛
𝑃
𝐭
italic-ϕ
𝐭
superscript
𝑒
⋅
imaginary-unit
𝐱
𝐭
𝐭
𝑃
𝐷
𝐹
𝐱
{\displaystyle{\displaystyle\frac{1}{(2\pi)^{n/2}}\int_{{\mathbb{R}^{n}}}P(% \mathbf{t})\phi(\mathbf{t})e^{\mathrm{i}\mathbf{x}\cdot\mathbf{t}}\mathrm{d}% \mathbf{t}=P(D)F(\mathbf{x}).}}
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