  A model-independent method for the analysis of the two-particle short-range
correlations is presented, that can be utilized to describe e.g. Bose-Einstein
(HBT), dynamical (ridge) or other correlation functions, that have a nearly
L\'evy or streched exponential shape. For the special case of L\'evy exponent
alpha = 1, the earlier Laguerre expansions are recovered, for the alpha = 2
special case, a new expansion method is obtained for nearly Gaussian
correlation functions. Multi-dimensional L\'evy expansions are also introduced
and their potential application to analyze rigde correlation data is discussed.
