  In this paper we present a complete asymptotic expansion of a symmetric
homogeneous stable (balanced), stabilizable and stabilized mean. By including
known asymptotic expansions of parametric means it is shown how the obtained
coefficients are used to solve the problem of identifying stable means within
classes of parametric means under consideration, how to disprove some mean is
stabilizable or stabilized and how to obtain best possible parameters such that
given mean is stabilizable with some pair of parametric means.
