A relation between h-index and impact factor in the power-law model

Theh-index (Hirsch, 2005) and the impact factor (Garfield, 2006) are undoubtedly the best-known scientometric indicators. It has been shown in previous articles that the idea of calculating an impact factor or an h-index can be applied to many source-item relations and in many timeframes (Egghe, in press; Egghe & Rousseau, 2006; Frandsen & Rousseau, 2005; Liang & Rousseau, in press; Rousseau, Guns, & Liu, 2008). The reader is referred to these articles for the exact definition of an h-index and an impact factor in the general case, i.e., using any time window. In this note we will propose a general relation (not a function!) in the power-law model. When stating that this relation is not a function we mean that many impact factors may correspond with one h-index value and vice versa.