Negentropy as a function of cumulants

Suppose f   is a density that is close to that of a standard normal, ϕϕ. For the first time, exact expressions are given for the negentropy, the differential entropy, and related quantities such as ∫-∞∞fr(x)/ϕr-1(x)dx for r=2,3,…r=2,3,… in terms of cumulants. Several advantages of our expressions over known ones are pointed out.