Dickman function

The Dickman function, denoted usually as \(\rho(u)\), is a special mathematical function that arises in number theory, particularly in the study of the distribution of prime numbers and in analytic number theory. It is defined for \(u \geq 0\) and can be expressed using the following piecewise definition: 1. For \(0 \leq u < 1\): \[ \rho(u) = 1 \] 2.