All

I have been looking around for a general way to solve the problem of $f(x+1) - f(x) = g(x)$, where $g(x)$ is given. Has this problem been studied before?

If there does not exist such a general way, could you please solve the following problem for me? I urgently want to know what $f(x)$ is.

$$ f(x+1) - f(x) = \frac{(1+\mu)^x}{1+(1+\nu)^{x-p}(1+\mu)^x} $$

where $\mu$, $\nu$ and $p$ are constants.

Your help is very much appreciated, thank you!