Question
a) If is entire such that
in
then show that f has the form
where
are constants with
.
Answer :
Word Count : 243
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Let ( f ) be an entire function such that ( f'(z) = f(z) ) for all ( z \in \mathbb{C} ). Since ( f ) is entire, it is holomorphic everywhere on the complex plane. The differential equation ( f'(z) = f(z) ) is a first-order linear differential equation, and its general solution can be found using standard methods of complex analysis. Consider the differential equation ( f'(z) - f(z) = 0 ). This
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