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Statements
U
(
-
n
-
1
2
,
z
)
=
D
n
(
z
)
=
e
-
1
4
z
2
𝐻𝑒
n
(
z
)
=
2
-
n
/
2
e
-
1
4
z
2
H
n
(
z
/
2
)
,
parabolic-U
𝑛
1
2
𝑧
Whittaker-D
𝑛
𝑧
superscript
𝑒
1
4
superscript
𝑧
2
Hermite-polynomial-He
𝑛
𝑧
superscript
2
𝑛
2
superscript
𝑒
1
4
superscript
𝑧
2
Hermite-polynomial-H
𝑛
𝑧
2
{\displaystyle{\displaystyle U\left(-n-\tfrac{1}{2},z\right)=D_{n}\left(z%
\right)=e^{-\frac{1}{4}z^{2}}\mathit{He}_{n}\left(z\right)=2^{-n/2}e^{-\frac{1%
}{4}z^{2}}H_{n}\left(z/\sqrt{2}\right),}}
n
=
0
,
1
,
2
,
…
𝑛
0
1
2
…
{\displaystyle{\displaystyle n=0,1,2,\dots}}
H
n
(
x
)
Hermite-polynomial-H
𝑛
𝑥
{\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
𝐻𝑒
n
(
x
)
Hermite-polynomial-He
𝑛
𝑥
{\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}
D
ν
(
z
)
Whittaker-D
𝜈
𝑧
{\displaystyle{\displaystyle D_{\NVar{\nu}}\left(\NVar{z}\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
U
(
a
,
z
)
parabolic-U
𝑎
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
