Solution of a recursion relation

[ledamage]

Hi there!

I wonder if there's an explicit solution to a recursion relation of the form

\alpha_{n+2} = A \alpha_{n+1} + B \alpha_n + C^n .

The solution of this recursion relation without C^n can easily be computed. I haven't found anything on the net.

Thanks!

 

[tiny-tim]

Hi there!

I wonder if there's an explicit solution to a recursion relation of the form

α_n+2 = A α_n+1 + B α_n + Cⁿ .

The solution of this recursion relation without Cⁿ can easily be computed. I haven't found anything on the net.

Thanks!

Hi ledamage!

You need to find a particular solution, exactly as if this was a differential equation.