2021/11/02 by Yik‐Man Chiang, Yik Man Chiang, Avery Ching +4
Computer Science · Engineering · Mathematics · Physics and Astronomy · #12J99 (secondary) #33C20 #33C80 12J20 (primary) #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Commutative Algebra and Its Applications #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math-ph #math.CA #math.MP #msc:12J20 #msc:12J99 #msc:33C20 #msc:33C80
paper · pdf · doi:10.48550/arxiv.2111.05103
Two more references are added; typos of minor natures are corrected on pages 7, 25 and 38
openalex publication_date 2021/11/02 · arxiv created 2021/11/17 · arxiv updated 2021/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a D-module approach to various kinds of solutions to several classes of important differential equations by long divisions of different differential operators. The zeros of remainder maps of such long divisions are handled by an analogue of Hensel's lemma established recently from valuation theory. In particular, this explains the common origin of some classically known special function series solutions of Heun equations and usual Frobenius series solutions. Moreover, these remainder maps also generate eigenvalue problems that lead to non-trivial factorizations of certain generalized hypergeometric operators.