The Hirsch index of a shifted Lotka function and its relation with the impact factor

Abstract

Based on earlier results about the shifted Lotka function, we prove an implicit functional relation between the Hirsch index (h-index) and the total number of sources (T). It is shown that the corresponding function, h(T), is concavely increasing. Next, we construct an implicit relation between the h-index and the impact factor IF (an average number of items per source). The corresponding function h(IF) is increasing and we show that if the parameter C in the numerator of the shifted Lotka function is high, then the relation between the h-index and the impact factor is almost linear.