Travel Inside a Funny Complex Differential Equation

We introduce a nonlinear, differential, complex multivariate equation with differences, which arises in several problems such as digital trees and data compression analysis. We courageously bring to evidence asymptotic estimates about this equation: in short, the logarithm of the function exists and has polynomial behaviour in so-called polynomial cones. Consequence of these results is the limiting normal distribution of the external path length in digital trees.