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Miklós Schweitzer
1953 Miklós Schweitzer
6
6
Part of
1953 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1953- Problem 6
Source: Miklós Schweitzer 1953- Problem 6
8/3/2015
6. Let
H
n
(
x
)
H_{n}(x)
H
n
(
x
)
be the nth Hermite polynomial. Find
lim
n
→
∞
(
y
2
n
)
n
H
n
(
n
y
)
\lim_{n \to \infty } (\frac{y}{2n})^{n} H_{n}(\frac{n}{y})
lim
n
→
∞
(
2
n
y
)
n
H
n
(
y
n
)
For an arbitrary real y. (S.5)
H
n
(
x
)
=
(
−
1
)
n
e
x
2
d
n
d
x
n
(
e
−
x
2
)
H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}\left(e^{{-x^2}}\right)
H
n
(
x
)
=
(
−
1
)
n
e
x
2
d
x
n
d
n
(
e
−
x
2
)
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