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math.QA2009
Formal calculus and umbral calculus
Thomas J. Robinson
In this paper we use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus and we introduce and s…
math.QA2009
New perspectives on exponentiated derivations, the formal Taylor theorem, and Faà di Bruno's formula
Thomas J. Robinson
We discuss certain aspects of the formal calculus used to describe vertex algebras. In the standard literature on formal calculus, the expression , where is not nece…
math.QA2009
On replacement axioms for the Jacobi identity for vertex algebras and their modules
Thomas J. Robinson
We discuss the axioms for vertex algebras and their modules, using formal calculus. Following certain standard treatments, we take the Jacobi identity as our main axiom and we reca…