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Statements
∫
x
∞
e
-
a
2
t
2
-
(
b
2
/
t
2
)
d
t
=
π
4
a
(
e
2
a
b
erfc
(
a
x
+
(
b
/
x
)
)
+
e
-
2
a
b
erfc
(
a
x
-
(
b
/
x
)
)
)
,
superscript
subscript
𝑥
superscript
𝑒
superscript
𝑎
2
superscript
𝑡
2
superscript
𝑏
2
superscript
𝑡
2
𝑡
𝜋
4
𝑎
superscript
𝑒
2
𝑎
𝑏
complementary-error-function
𝑎
𝑥
𝑏
𝑥
superscript
𝑒
2
𝑎
𝑏
complementary-error-function
𝑎
𝑥
𝑏
𝑥
{\displaystyle{\displaystyle\int_{x}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}%
\mathrm{d}t=\frac{\sqrt{\pi}}{4a}\left(e^{2ab}\operatorname{erfc}\left(ax+(b/x%
)\right)+e^{-2ab}\operatorname{erfc}\left(ax-(b/x)\right)\right),}}
|
ph
a
|
<
1
4
π
phase
𝑎
1
4
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}
x
>
0
𝑥
0
{\displaystyle{\displaystyle x>0}}
|
ph
a
|
<
1
4
π
ph
𝑎
1
4
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}
π
{\displaystyle{\displaystyle\pi}}
erfc
z
complementary-error-function
𝑧
{\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
x
𝑥
{\displaystyle{\displaystyle x}}
