Year: 2010
Type: preprint
Abstract: We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of logarithmic intertwining operators and logarithmic tensor category theory for modules for a vertex operator algebra. This extension has a variety of interesting arithmetic properties. We develop one such result here, the aforementioned recursive identity. We have applied this identity elsewhere to certain formal series expansions related to a general formal Taylor theorem and these series expansions in turn yield a sequence of combinatorial identities which have as special cases certain classical combinatorial identities involving (separately) the Stirling numbers of the first and second kinds.
Source: arXiv (Cornell University)
Author: Robinson, Thomas J.
Institution: Rutgers, The State University of New Jersey
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1624725626