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Miklós Schweitzer
2018 Miklós Schweitzer
9
9
Part of
2018 Miklós Schweitzer
Problems
(1)
Sequence of derivatives converges pointwise
Source: Miklós Schweitzer 2018 P9
11/18/2018
Let
f
:
C
→
C
f:\mathbb{C} \to \mathbb{C}
f
:
C
→
C
be an entire function, and suppose that the sequence
f
(
n
)
f^{(n)}
f
(
n
)
of derivatives converges pointwise. Prove that
f
(
n
)
(
z
)
→
C
e
z
f^{(n)}(z)\to Ce^z
f
(
n
)
(
z
)
→
C
e
z
pointwise for a suitable complex number
C
C
C
.
calculus
derivative
college contests
Miklos Schweitzer
complex analysis