Formal Iterated Logarithms and Exponentials and the Stirling Numbers
Thomas J. Robinson
TL;DR
This paper explores the algebraic structure of formal iterated logarithms and exponentials, revealing how Stirling numbers naturally arise as expansion coefficients in their formal analytic expansions.
Contribution
It introduces a novel connection between formal iterated logarithmic/exponential variables and Stirling numbers through their analytic expansions.
Findings
Stirling numbers appear as coefficients in formal expansions.
The algebraic structure of iterated logs/exponentials involves Stirling numbers.
Extensions of Stirling numbers are relevant in this context.
Abstract
We calculate the formal analytic expansions of certain formal translations in a space of formal iterated logarithmic and exponential variables. The results show how the algebraic structure naturally involves the Stirling numbers of the first and second kinds, and certain extensions of these, which appear as expansion coefficients.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics