- E32
[1SK] Prerequisites:[19M], [1SF].
Fix \(π,πββ\) with \(πβ π\), \(q(x)\) a polynomial, and \(kββ\). Letβs define \(p(x)=(x-π)^ k\). Show that
\[ p(D)f(x)=e^{π x}q(x) \]if and only if
\[ f(x)=e^{π x} r(x) + e^{π x} \tilde q(x) ~ , \]with \(r\) polynomial of degree at most \(k-1\) and \(\tilde q\) polynomial of the same degree as \(q\).
Solution 1
EDB β 1SK
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English
Authors:
"Mennucci , Andrea C. G."
.
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