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

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.

References in corpus (4)

• New solutions of Heun general equation
• Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
• Single polymer dynamics in elongational flow and the confluent Heun equation
• New relations for the derivative of the confluent Heun function

Cited by in corpus (4)

• Calabi-Yau Feynman integrals in gravity: $\epsilon$-factorized form for apparent singularities
• Generalized hypergeometric solutions of the Heun equation
• From Heun Class Equations to Painlevé Equations
• Series solutions of confluent Heun equations in terms of incomplete Gamma-functions