Would anyone be able to recommend a book for solutions to difference equations of the first and second order, homogenous and non-homogenous. I'm not after anything too in depth but my probability course uses a lot of these and non of my calculus classes so far have mentioned these.
examples of the difference equations I have come across:
\begin{aligned} t_k & =\mathbb{E}\left(T \mid X_1=1\right) \frac{1}{2}+\mathbb{E}\left(T \mid X_1=-1\right) \frac{1}{2} \\ & =\left(1+t_{k+1}\right) \frac{1}{2}+\left(1+t_{k-1}\right) \frac{1}{2} \end{aligned} $$t_0=0, \quad t_m=0 \text {. }$$
$$t_{k+1}-2 t_k+t_{k-1}=-2 .$$