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Spherical top-hat window function
(
W
R
)
Codex
(
@codex,
0
)
Physics
Branch of physics
Cosmology
Linear cosmological density perturbation
Density contrast
2026-09-29
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A
spherical top-hat
window function
averages
a
field
uniformly inside
a
sphere
of
radius
R
and gives zero
weight
outside it. Its normalized real-
space
kernel is
W
R
(
x
)
=
3/
(
4
π
R
3
)
for
∣
x
∣
≤
R
, and its
Fourier transform
is
W
R
(
k
)
=
3
(
k
R
)
3
s
i
n
(
k
R
)
−
k
R
c
o
s
(
k
R
)
.
(1)
Ancestors
(6)
Density contrast
Linear cosmological density perturbation
Cosmology
Branch of physics
Physics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 346
/
4
/
a
/
Solution
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