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Statements
∫
a
b
e
i
x
t
q
(
t
)
d
t
∼
e
i
a
x
∑
s
=
0
∞
q
(
s
)
(
a
)
(
i
x
)
s
+
1
-
e
i
b
x
∑
s
=
0
∞
q
(
s
)
(
b
)
(
i
x
)
s
+
1
,
asymptotic-expansion
superscript
subscript
𝑎
𝑏
superscript
𝑒
𝑖
𝑥
𝑡
𝑞
𝑡
𝑡
superscript
𝑒
𝑖
𝑎
𝑥
superscript
subscript
𝑠
0
superscript
𝑞
𝑠
𝑎
superscript
𝑖
𝑥
𝑠
1
superscript
𝑒
𝑖
𝑏
𝑥
superscript
subscript
𝑠
0
superscript
𝑞
𝑠
𝑏
superscript
𝑖
𝑥
𝑠
1
{\displaystyle{\displaystyle\int_{a}^{b}e^{ixt}q(t)\mathrm{d}t\sim e^{iax}\sum%
_{s=0}^{\infty}q^{(s)}(a)\left(\frac{i}{x}\right)^{s+1}-e^{ibx}\sum_{s=0}^{%
\infty}q^{(s)}(b)\left(\frac{i}{x}\right)^{s+1},}}
x
→
+
∞
→
𝑥
{\displaystyle{\displaystyle x\to+\infty}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
q
(
t
)
𝑞
𝑡
{\displaystyle{\displaystyle q(t)}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
Identifiers
