The Hirsch Function and its Properties

The Hirsch function, denoted as h(f), of a given continuous function f is a new function depending on a parameter. It exists provided some assumptions are satisfied. If this parameter takes the value one, we obtain the well-known h-index. We prove several properties of the Hirsch function and characterize the shape of general functions that are Hirsch functions. We, moreover, present a formula that enables the calculation of f, given its Hirsch function h(f).