Extragalactic backgrounds .1. General formalism

The general formalism relevant for studies of the contributions to the background of extragalactic sources is summarized. Analytic formulae, useful to highlight some basic aspects, are presented; many of them were, to our knowledge, never published before. In particular we point out and discuss the effect on source counts of a luminosity dependent K-correction, such as that appropriate for rich clusters of galaxies, and of a spectrum steeply increasing towards high frequencies as is the case for the sub-mm/mm spectrum of galaxies. Also we derive simple analytic approximations useful to compute the contribution of clustering to small scale fluctuations.