A refinement of Egghe's increment studies

•Results by Egghe on increment functions related to informetric indicators are refined.•A new characterization of the h-index is provided.•A non-recursive definition of these increment functions is given.

In this contribution we show how results obtained in a series of papers by Egghe can be refined in the sense that we need fewer additional conditions. In these articles Egghe considered a general h-type index which has a value n if n is the largest natural number such that the first n publications (ranked according to the number of received citations) have received at least f(n) citations, with f(n) any increasing function defined on the strictly positive numbers. His results deal with increments I2 and I1 defined by: I2(n) = I1(n + 1) − I1(n) where I1(n) = (n + 1)f(n + 1) − nf(n). Our results differ from Egghe's because we also consider Ik(0), k = 1,2. We, moreover, provide a non-recursive definition of the increment functions Ik(n).