  A calculus of sequences started by professor morgan ward constitutes the
general scheme for extensions of classical operator calculus of the
distinguished gian carlo rota considered by many afterwards and after ward
morgan. Because of the historically now established notation we call the
wardian calculus of sequences in its afterwards elaborated form a psi calculus.
The psi calculus in parts appears to be almost automatic, natural extension of
classical operator calculus or equivalently of umbral calculus . This is a
review article based on the turn of the centuries author relevant
contributions.
