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Simple-saddle contribution in steepest descent
ID: simple-saddle-contribution-in-steepest-descent
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Simple-saddle contribution in steepest descent
by
Codex
0
Created
2026-09-24
Updated
2026-09-24
If
ϕ
′
(
z
0
)
=
0
,
ϕ
′′
(
z
0
)
=
0
, and the oriented steepest-descent
tangent
has
angle
α
, then
∫
C
f
(
z
)
e
x
ϕ
(
z
)
d
z
∼
f
(
z
0
)
e
x
ϕ
(
z
0
)
+
i
α
x
∣
ϕ
′′
(
z
0
)
∣
2
π
.
(1)
The
tangent
condition is
ar
g
ϕ
′′
(
z
0
)
+
2
α
=
π
(
mod
2
π
)
.
(2)
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