I've got two questions.
I'm trying to extract the "coefficients" of a power series. I think my terminology is incorrect here but here is what I mean.
Here are some examples
- A(Z) = 1/(1-Z) a(n) = 1;
- A(Z) = 1/(1-Z)^2, a(n) = (n + 1)
- A(Z) = 1/(1-z)^3 a(n) = (1/2)(n+1)(n+2)
But how do I express something like this in terms of a(n) (i need it to solve recurrence relatoins).
- A(Z) = 5*Z a(n) = ??
- A(Z) = 5 a(n) = ??
The last term is just a constant (I used 5 as an example) and the second last time is a constant multiplied by Z.
Any help would be most appreciated.
Thanks
If $A(z)=5z$, then $$a(n)=\begin{cases}5,&\text{if }n=1\\0,&\text{otherwise}\;.\end{cases}$$ If $A(z)=5$, change the first case to $n=0$ instead of $n=1$.
If you know about Iverson brackets, you can write the first more simply as $a(n)=5[n=1]$ and the second as $5[n=0]$.