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Mathematics
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Complex Analysis
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Liouville's Theorem
Liouville's Theorem
A surprising and powerful result about holomorphic functions.
📜
The statement of the theorem
Every bounded entire function must be constant.\n
∣
f
(
z
)
∣
≤
M
⟹
f
(
z
)
=
c
|f(z)| \le M \implies f(z) = c
∣
f
(
z
)
∣
≤
M
⟹
f
(
z
)
=
c
Source: Wikipedia