Suppose that R is a commutative Noetherian ring with non-zero identity. The main goal of this note is characterizing left and right derived functors of special local cohomology modules (or their Matlis duals) by means of left and right derived functors (or Matlis duals) of R (x) , where x := x1, . . . , xn is a standard system of parameters for R. In this way, we exploit of the relations between their syzygies.
