Dynamic h ‐index: The Hirsch index in function of time

When there are a group of articles and the present time is fixed we can determine the unique number h being the number of articles that received h or more citations while the other articles received a number of citations which is not larger than h . In this article, the time dependence of the h ‐index is determined. This is important to describe the expected career evolution of a scientist's work or of a journal's production in a fixed year. We use the earlier established cumulative n th citation distribution. We show that$$ h = ((1 - a^t )^{\alpha - 1} T)^{{1 \over \alpha }} $$ where a is the aging rate, α is the exponent of Lotka's law of the system, and T is the total number of articles in the group. For t = +∞ we refind the steady state (static) formula $h = T^{{1 \over \alpha }}$ , which we proved in a previous article. Functional properties of the above formula are proven. Among several results we show (for α, a , T fixed) that h is a concavely increasing function of time, asymptotically bounded by $T^{{1 \over \alpha }}$ .