  This paper gives a coherent and comprehensive review of the results
concerning the inverse Langevin L(x) and Brillouin functions B_J (x) and of the
inverse of L(x)/x and B_J (x)/x. As these functions are used in several fields
of physics, without evident interconnections - magnetism (ferromagnetism,
superparamagnetism, nanomagnetism, hysteretic physics), rubber elasticity,
rheology, solar energy conversion - the new results are not always efficiently
transferred from a domain to another. The increasing accuracy of experimental
investigations claims an increasing accuracy in the knowledge of these
functions, so it is important to compare the accuracy of various approximants
and even to obtain, in some cases, the exact form of the inverses of L(x), B_J
(x), L(x)/x and B_J (x)/x. This exact form can be obtained, in some cases, at
least in principle, using the recently developed theory of generalized Lambert
functions; in some particular - and also relevant - cases, explicit expressions
for these new special functions are obtained. The paper contains also some new
results, concerning both exact and approximate forms of the aforementioned
inverse functions.
