Time-dependent Lotkaian informetrics incorporating growth of sources and items

In a previous article, static Lotkaian theory was extended by introducing a growth function for the items. In this article, a second general growth function–this time for the sources–is introduced. Hence this theory now comprises real growth situations, where items and sources grow, starting from zero, and at possibly different paces. The time-dependent size- and rank-frequency functions are determined and, based on this, we calculate the general, time-dependent, expressions for the hh- and gg-index. As in the previous article we can prove that both indices increase concavely with a horizontal asymptote, but the proof is more complicated: we need the result that the generalized geometric average of concavely increasing functions is concavely increasing.