An interesting discovery, thanks to a problem presented by K. Srinivasa Raghava:
A standard result for real, where is the floor function:
Now it so happens that:
which is of course intuitive owing to Riemann surfaces produced by the complex logarithm. I could not find the result but I am nearly certain it must be somewhere.
Now to get an idea, let us examine the compensating function
And of course, the complex logarithm (here is the standard function, just to illustrate):