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Handout 9.2 Homogeneous Recurrence Equations
Example 9.3. Solving Advancement Operator Equations.
Solve the advancement operator equation
\begin{equation*}
(A+4)f=0
\end{equation*}
with the initial condition \(f(0)=2\text{.}\)
Example 9.4. Applying Advancement Operator Polynomials.
Let
\(c_{1}\) and
\(c_{2}\) be constants and define
\(f(n) = c_{1}3^{n} +c_{2}(-4)^{n}\text{.}\) Compute
\((A+4)(A-3)f(n)\text{.}\)
Proposition 9.5.
The solution to the advancement operator equation
\begin{equation*}
(A-b_{1})(A-b_{2})\cdots (A-b_{k})f(n) = 0
\end{equation*}
where \(b_{i}\neq b_{j}\) if \(i\neq j\) is .
Note: When solving
\begin{equation*}
p(A)f(n)=g(n)
\end{equation*}
we’ll focus on \(p(0)\neq 0\text{.}\) Any factors of \(A\) in \(p(A)\) could be dealt with by shifting solutions.
