Binomial convolution and transformations of Appell polynomials

We show that the set A of Appell sequences is an abelian group under the binomial convolution. This is essentially equivalent to other approaches considered in the literature, in particular, the determinantal approach. We also define a scale transformation Tα:A→A, which is an isomorphism, and a transformation RY:A→A based on expectations with respect to a random variable Y. Using these tools, we give explicit formulas for the determinantal form of Appell sequences, as well as for the formula of representation of powers and the Srivastava-Pintér addition theorem. Various illustrative examples, mainly referring to various generalizations of Bernoulli and Euler polynomials, are discussed in detail.