- E22
[1VG] Note:exercise 4, written exam, June 23th, 2012.
A function \(f (x) =β_{n=0}^β a_ n x_ n\), analytic in a neighborhood of 0, satisfies on its domain the conditions
\[ \begin{cases} f β (x) = 1 + f (βx)\\ f (0) = c \end{cases} \quad ; \](note that this is not a Cauchy problem!).
Determine \(f\).
Prove that the function found is the only solution, in the set of all functions that can be derived in a neighborhood of 0.
EDB β 1VG
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Authors:
"Mennucci , Andrea C. G."
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