2021/11/23 by Dominic C. Milioto, Milioto, Dominic C.
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis #Primary 1401 #Secondary 1404
paper · pdf · doi:10.48550/arxiv.2111.11883
openalex publication_date 2021/11/23 · openalex created_date 2022/07/20 · openalex updated_date 2026/07/28
The purpose of this paper is to introduce the branching geometry of algebraic\nfunctions around singular points and to describe a simple method of determining\nradii of convergence of their power expansions in terms of those singular\npoints. Branching geometries are categorized into six types. Then a method is\npresented to determine radii of convergence of branch power expansions using\nanalytic continuation and the identification of convergence-limiting singular\npoints. Test cases exhibiting a variety of branching morphologies are analyzed,\nand convergence results obtained through analytic continuation are checked\nagainst Root Tests of the associated power series. All Root Tests agreed well\nwith the results obtained by analytic continuation. Mathematica ver. 12.3 was\nused to implement the numeric algorithms.\n