Apologies if this has already been asked, but I'm stuck.
I have a recurrance relation that I want resolve to the form $a_n=f(n,\gamma)a_0$ but I don't know what to do.
The relation is: $$a_n=a_{n-1}\frac{n-1-\gamma}{n^2}$$ where $\gamma$ is not an integer.
There is obviously a $(n!)^2$ term on the bottom. I don't know how to deal with the top, seeing as it is not going to be an integer. I'm thinking there has to be something to do with gamma functions, but there are some tricky things that happen depending on the value of $\gamma$ you choose. (for instance, the sign flipping in the sequence if $\gamma>0$).
Please help!
For future reference of anyone who comes across this, the solution uses the Pochhammer symbol.
$$a_n=\frac{(-\gamma+n-1)_n}{(n!)^2}a_0=\frac{(-\gamma)^{(n)}}{(n!)^2}a_0$$
Where $(x)_n$ is the falling factorial and $x^{(n)}$ is the rising factorial