Deviation of a local ring

In commutative algebra, the deviations of a local ring "R" are certain invariants ε"i"("R") that measure how far the ring is from being regular.
Definition.
The deviations ε"n" of a local ring "R" with residue field "k" are non-negative integers defined in terms of its Poincaré series "P"("t") by 
The zeroth deviation ε0 is the embedding dimension of "R" (the dimension of its tangent space). The first deviation ε1 vanishes exactly when the ring "R" is a regular local ring, in which case all the higher deviations also vanish. The second deviation ε2 vanishes exactly when the ring "R" is a complete intersection ring, in which case all the higher deviations vanish.