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Statements
∫
-
∞
∞
H
m
(
y
)
e
-
y
2
H
n
(
x
-
y
)
e
-
(
x
-
y
)
2
d
y
=
π
1
2
2
-
1
2
(
m
+
n
+
1
)
H
m
+
n
(
2
-
1
2
x
)
e
-
1
2
x
2
.
superscript
subscript
Hermite-polynomial-H
𝑚
𝑦
superscript
𝑒
superscript
𝑦
2
Hermite-polynomial-H
𝑛
𝑥
𝑦
superscript
𝑒
superscript
𝑥
𝑦
2
𝑦
superscript
𝜋
1
2
superscript
2
1
2
𝑚
𝑛
1
Hermite-polynomial-H
𝑚
𝑛
superscript
2
1
2
𝑥
superscript
𝑒
1
2
superscript
𝑥
2
{\displaystyle{\displaystyle\int_{-\infty}^{\infty}H_{m}\left(y\right)e^{-y^{2%
}}H_{n}\left(x-y\right)e^{-(x-y)^{2}}\mathrm{d}y=\pi^{\frac{1}{2}}2^{-\frac{1}%
{2}(m+n+1)}H_{m+n}\left(2^{-\frac{1}{2}}x\right)e^{-\frac{1}{2}x^{2}}.}}
H
n
(
x
)
Hermite-polynomial-H
𝑛
𝑥
{\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
y
𝑦
{\displaystyle{\displaystyle y}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
