More on the Bernoulli and Taylor Formula for Extended Umbral Calculus

One presents here the * ψ-Bernoulli-Taylor* formula of a new sort with the rest term of the Cauchy type recently derived by the author in the case of the so called ψ-difference calculus which constitutes the representative for the purpose case of extended umbral calculus. The central importance of such a type formulas is beyond any doubt-and recent publications do confirm this historically established experience .Its links via umbrality to combinatorics are known at least since Rota and Mullin-Rota source papers then up to recently extended by many authors to be indicated in the sequel.