Time-dependent Lotkaian informetrics incorporating growth of sources and items

Abstract

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 h- and g-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.