I discovered this notation in the problem outlined below. My confusion lies in the subscript notation used on the I's, i.e. the $n$ and $n-1$ in $I_n$ and $I_{n-1}$
Show that if $I_n$ is defined by the integral
$$I_n = \int_{0}^\infty x^ne^{-x} dx$$
where $n$ is a positive integer, then
$$I_n = nI_{n-1}$$
After integrating $I_n$ by parts, the final line of the proof is as follows:
$$I_n = 0+n\int_{0}^\infty x^{n-1}e^{-x} dx = nI_{n-1}$$
With this result, I would assume that the subscript notation says to replace $n$ with $n-1$. But a more formal definition of what this notation means is what I'm looking for.