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Statements
H
n
(
x
)
=
2
n
U
(
-
1
2
n
,
1
2
,
x
2
)
=
2
n
x
U
(
-
1
2
n
+
1
2
,
3
2
,
x
2
)
=
2
1
2
n
e
1
2
x
2
U
(
-
n
-
1
2
,
2
1
2
x
)
.
Hermite-polynomial-H
𝑛
𝑥
superscript
2
𝑛
Kummer-confluent-hypergeometric-U
1
2
𝑛
1
2
superscript
𝑥
2
superscript
2
𝑛
𝑥
Kummer-confluent-hypergeometric-U
1
2
𝑛
1
2
3
2
superscript
𝑥
2
superscript
2
1
2
𝑛
superscript
𝑒
1
2
superscript
𝑥
2
parabolic-U
𝑛
1
2
superscript
2
1
2
𝑥
{\displaystyle{\displaystyle H_{n}\left(x\right)=2^{n}U\left(-\tfrac{1}{2}n,%
\tfrac{1}{2},x^{2}\right)=2^{n}xU\left(-\tfrac{1}{2}n+\tfrac{1}{2},\tfrac{3}{2%
},x^{2}\right)=2^{\frac{1}{2}n}e^{\frac{1}{2}x^{2}}U\left(-n-\tfrac{1}{2},2^{%
\frac{1}{2}}x\right).}}
H
n
(
x
)
Hermite-polynomial-H
𝑛
𝑥
{\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
U
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
U
(
a
,
z
)
parabolic-U
𝑎
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
