The h-index formalism

This article provides an overview of the development of the h-index formalism. We begin with the original formulation as provided by Hirsch and move on to the latest versions. In this we show how the h-index formalism has evolved over time. Lesser known versions, in particular the continuous version of the h-index is brought to the front. We also discuss the Prathap–Kosmulski–Schubert successive h-indices. As announced in the title we focus on the h-index formalism, omitting generalizations, such as the g-index, and applications in research assessment.