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Statements
⟨
ℱ
(
H
)
,
ϕ
⟩
=
π
2
ϕ
(
0
)
+
i
2
π
⨍
-
∞
∞
ϕ
(
x
)
x
d
x
.
distribution
distributional-Fourier-transform
Heaviside-H
italic-ϕ
2
italic-ϕ
0
imaginary-unit
2
subscript
superscript
principal-value-integral
italic-ϕ
𝑥
𝑥
𝑥
{\displaystyle{\displaystyle\left\langle\mathscr{F}\left(H\right),\phi\right%
\rangle=\sqrt{\frac{\pi}{2}}\phi(0)+\frac{\mathrm{i}}{\sqrt{2\pi}}\pvint^{%
\infty}_{-\infty}\frac{\phi(x)}{x}\mathrm{d}x.}}
H
(
x
)
Heaviside-H
𝑥
{\displaystyle{\displaystyle H\left(\NVar{x}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
⟨
Λ
,
ϕ
⟩
distribution
Λ
italic-ϕ
{\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right%
\rangle}}
ℱ
(
u
)
distributional-Fourier-transform
𝑢
{\displaystyle{\displaystyle\mathscr{F}\left(\NVar{u}\right)}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
⨍
a
b
superscript
subscript
principal-value-integral
𝑎
𝑏
{\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
ϕ
(
x
)
italic-ϕ
𝑥
{\displaystyle{\displaystyle\phi(x)}}
Identifiers
