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

@article{Slavyanov2016GenerationAR,
  title={Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients},
  author={Sergey Slavyanov and Daria Satco and Artur M. Ishkhanyan and T. A. Rotinyan},
  journal={Theoretical and Mathematical Physics},
  year={2016},
  volume={189},
  pages={1726-1733}
}
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. 

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Symmetries and apparent singularities for the simplest Fuchsian equations

  • S. Slavyanov
  • Mathematics
    Theoretical and Mathematical Physics
  • 2017
We consider the simplest Fuchsian second-order equations with particular attention to the role of apparent singularities. We show the relation to the Painlevé equation and follow the matrix

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