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

S. Yu. Slavyanov; D. A. Satco; A. M. Ishkhanyan; T. A. Rotinyan

doi:10.1134/S0040577916120059

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

Authors: Slavyanov S.Y.¹, Satco D.A.¹, Ishkhanyan A.M.²^,3, Rotinyan T.A.¹
Affiliations:
1. St. Petersburg State University
2. Institute for Physical Research
3. Institute of Physics and Technology
Issue: Vol 189, No 3 (2016)
Pages: 1726-1733
Section: Article
URL: https://journals.rcsi.science/0040-5779/article/view/170875
DOI: https://doi.org/10.1134/S0040577916120059
ID: 170875

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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.