Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients

TL;DR

This paper explores how apparent singularities in linear differential equations with polynomial coefficients can be generated or removed, providing conjectures and examples relevant to Fuchsian equations and polymer physics.

Contribution

It introduces conjectures on the generation and removal of apparent singularities in Fuchsian differential equations with polynomial coefficients.

Findings

Examples of generating apparent singular points through differentiation.

Formulation of two conjectures on singularity manipulation.

Application to a model problem in polymer physics.

Abstract

We discuss several examples of generating apparent singular points as a result of differentiating particular homogeneous linear ordinary differential equations with polynomial coefficients and formulate two general conjectures on the generation and removal of apparent singularities in arbitrary Fuchsian differential equations with polynomial coefficients. We consider a model problem in polymer physics.