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math.AC2025
On Riordan groups involving formal semi-Laurent series and their Lie group structure
Dariusz Bugajewski, Dawid Bugajewski, Xiao-Xiong Gan +1
The main goal of this paper is to introduce and to investigate properties of generalized Riordan arrays and generalized Riordan groups that involve formal semi-Laurent series. In p…
math.AC2023
On the recursive and explicit form of the general J.C.P. Miller formula with applications
Dariusz Bugajewski, Dawid Bugajewski, Xiao-Xiong Gan +1
The famous J.C.P. Miller formula provides a recurrence algorithm for the composition , where is the formal binomial series and is a formal power series, howe…
math.AC2022
The inverse and the composition in the set of formal Laurent series
Dawid Bugajewski
The aim of this article is to investigate the issues of multiplicative inverses and composition in the set of formal Laurent series. We show the lack of general uniqueness of inver…