S. Yu. Slavyanov, D. F. Shat'ko, A. M. Ishkhanyan, T. A. Rotinyan, “Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients”, TMF, 2016, Volume 189, Number 3,Pages <nobr>371

This article is cited in 10 papers

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

S. Yu. Slavyanov^a, D. F. Shat'ko^a, A. M. Ishkhanyan^bc, T. A. Rotinyan^a

^a Saint Petersburg State University, Saint Petersburg, Russia
^b Institute of Physics and Technology, Tomsk Polytechnical University, Tomsk. Russia
^c Institute for Physical Research, National Academy of Sciences of Armenia, Ashtarak-2, Armenia

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.

Keywords: Heun-class equation, Painlevé equation, apparent singular point.

Received: 13.05.2016

DOI: 10.4213/tmf9229