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arXiv · 1012.0822

A recursion identity for formal iterated logarithms and iterated exponentials

Thomas J. Robinson
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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.

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Thomas J. Robinson. 2010-12-03. A recursion identity for formal iterated logarithms and iterated exponentials. https://arxiv.org/abs/1012.0822

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