Exact entropy series representation for blind source separation

An explicit infinite series for the marginal entropy of a probability density function is developed. The series includes all orders of statistics and employs both the Gram-Charlier and the Edgeworth expansions for its derivation. The derivation exploits the fact that the two expansions are equivalent for the same probability density. The developed entropy series expression can be used to express the averaged mutual information to any degree of accuracy. This measure is then used in the derivation of the update laws of the blind separation of sources.