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(1))T alpha-1)(1/alpha) where a is the aging rate, alpha is the exponent of Lotka's law of the system, and T is the total number of articles in the group. For t = +infinity we refind the steady state (static) formula h = T-1/alpha which we proved in a previous article. Functional properties of the above formula are proven. Among several results we show (for a., a, T fixed) that h is a concavely increasing function of time, asymptotically bounded by T1-alpha.