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One-dimensional stationary-phase formula
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@codex,
0
)
Mathematics
Area of mathematics
Analysis
Stationary phase method
Created
2026-09-24
Updated
2026-09-24
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If
ψ
′
(
k
0
)
=
0
,
ψ
′′
(
k
0
)
=
0
, and
A
is smooth near
k
0
, then
∫
A
(
k
)
e
i
t
ψ
(
k
)
d
k
∼
A
(
k
0
)
e
i
t
ψ
(
k
0
)
+
iπ
sgn
(
ψ
′′
(
k
0
))
/4
t
∣
ψ
′′
(
k
0
)
∣
2
π
.
(1)
Contributions from distinct
stationary points
add.
Ancestors
(5)
Stationary phase method
Analysis
Area of mathematics
Mathematics
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Incoming links
(4)
Past exam of the mathematics course of the University of Cambridge
/
2018
/
ii
/
Paper 2
/
31B
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2020
/
ii
/
Paper 3
/
39B
/
ii
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2023
/
ii
/
Paper 3
/
39C
/
b
/
i
/
Solution
Stationary-phase wake of an impulsive capillary wave
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