On the Generalized Lambert Function
Speaker:
Alex Kreinin, University of Toronto, Andrey Marchenko, Vladimir Vinogradov, Ohio University and University of Toronto
Date and Time:
Monday, May 12, 2025 - 3:00pm to 4:00pm
Location:
Fields Institute, Room 210
Abstract:
We consider a particular generalized Lambert function, $y(x)$, defined by the implicit equation $ y^\beta = 1 - e^{-xy}$, with $x>0$ and $ \beta > 1$. Solutions to this equation can be found in terms of a certain continued exponential. Asymptotic and structural properties of a non-trivial solution, $y_\beta(x)$, and its connection to the extinction probability of related branching processes are discussed. We demonstrate that this function constitutes a cumulative distribution function of a previously unknown non-negative absolutely continuous random variable. Based on our joint paper