Characterization of Delta Operator for Appell Polynomials

In this paper, we introduce a new approach for the Appell polynomials via the sequential representation of the delta operator. Moreover, a theorem which gives the necessary condition for Appell polynomials is proposed. The main objective of this paper is to investigate the characterization of the delta operator for the Bernoulli, the Hermite and the Genocchi polynomials. From our investigation, we are able to prove many interesting propositions for the above mentioned.