Towards psi-extension of Rota`s Finite Operator Calculus
  A class of extended umbral calculi in operator form is presented. Extensions of all basic theorems of classical Finite Operator Calculus are shown to hold. The impossibility of straightforward extending of quantum q-plane formulation of the q-umbral caculus to the general psi-calculus case is demonstrated. 
A. K. Kwasniewski