The algebra for formal series. II. Sheffer sequences

In this paper we continue the study of the algebra of formal series. We will develop some new results on special sequences and begin the study of Sheffer Sequences, discussing the important examples of Hermite, Laguerre and Bernoulli. The second section gives a very brief survey of parts of [I] as well as a new result which will be used in the sequel. A general remark about the theory is in order. Sequences of polynomials of binomial and Sheffer type-such as those of Hermite, Laguerre and Bernoulli-have played a key role in the theory of special functions. It is the yoga of the algebra of formal series that these sequences are but the polynomial tip of corresponding sequences of Laurent series with a finite number of terms of positive degree. By corresponding we mean that the sequences of Laurent series possess many of the same algebraic properties as the sequences of polynomials To be absolutely plain, to each sequence of polynomials of Sheffer type (which includes binomial type)