Formal multiplicative root series and algorithms of their evaluation. Issue 8 (7th July 2021)

• Record Type: Journal Article
• Authors: Gan, Xiao-Xiong; Bugajewski, Dariusz
• Is Part Of: Communications in algebra. Volume 49:Issue 8(2021)
• Page Start: 3232
• Page End: 3240
• Publication Date: 2021-07-07
• Subjects: Formal power series -- formal root series -- iterative root -- Multinomial Theorem; Primary: 13F25 -- Secondary: 26E35; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1892711
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In this paper we provide necessary and sufficient conditions for a formal power series g over R or C to have formal power series g 1 / k such that ( g 1 / k ) k = g for all positive integers k or for some positive integers. The algorithms of computing such formal root series are also provided. Moreover, we investigate the uniqueness of formal root series if there exists.