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Statements
∫
a
b
e
i
x
p
(
t
)
q
(
t
)
d
t
∼
e
i
x
p
(
a
)
∑
s
=
0
∞
exp
(
(
s
+
λ
)
π
i
2
μ
)
Γ
(
s
+
λ
μ
)
b
s
x
(
s
+
λ
)
/
μ
-
e
i
x
p
(
b
)
∑
s
=
0
∞
P
s
(
b
)
(
i
x
)
s
+
1
,
asymptotic-expansion
superscript
subscript
𝑎
𝑏
superscript
𝑒
𝑖
𝑥
𝑝
𝑡
𝑞
𝑡
𝑡
superscript
𝑒
𝑖
𝑥
𝑝
𝑎
superscript
subscript
𝑠
0
𝑠
𝜆
𝜋
𝑖
2
𝜇
Euler-Gamma
𝑠
𝜆
𝜇
subscript
𝑏
𝑠
superscript
𝑥
𝑠
𝜆
𝜇
superscript
𝑒
𝑖
𝑥
𝑝
𝑏
superscript
subscript
𝑠
0
subscript
𝑃
𝑠
𝑏
superscript
𝑖
𝑥
𝑠
1
{\displaystyle{\displaystyle\int_{a}^{b}e^{ixp(t)}q(t)\mathrm{d}t\sim e^{ixp(a%
)}\sum_{s=0}^{\infty}\exp\left(\frac{(s+\lambda)\pi i}{2\mu}\right)\Gamma\left%
(\frac{s+\lambda}{\mu}\right)\frac{b_{s}}{x^{(s+\lambda)/\mu}}-e^{ixp(b)}\sum_%
{s=0}^{\infty}P_{s}(b)\left(\frac{i}{x}\right)^{s+1},}}
x
→
+
∞
→
𝑥
{\displaystyle{\displaystyle x\to+\infty}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
exp
z
𝑧
{\displaystyle{\displaystyle\exp\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
p
(
t
)
𝑝
𝑡
{\displaystyle{\displaystyle p(t)}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
P
s
(
t
)
subscript
𝑃
𝑠
𝑡
{\displaystyle{\displaystyle P_{s}(t)}}
q
(
t
)
𝑞
𝑡
{\displaystyle{\displaystyle q(t)}}
λ
𝜆
{\displaystyle{\displaystyle\lambda}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
Identifiers
