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.

Original language	English
Pages (from-to)	1726-1733
Number of pages	8
Journal	Theoretical and Mathematical Physics
Volume	189
Issue number	3
DOIs	https://doi.org/10.1134/S0040577916120059
Publication status	Published - 1 Dec 2016

Keywords

apparent singular point
Heun-class equation
Painlevé equation

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1134/S0040577916120059

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title = "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.",

keywords = "apparent singular point, Heun-class equation, Painlev{\'e} equation",

author = "Slavyanov, {S. Yu} and Satco, {D. A.} and Ishkhanyan, {A. M.} and Rotinyan, {T. A.}",

year = "2016",

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AU - Slavyanov, S. Yu

AU - Satco, D. A.

AU - Ishkhanyan, A. M.

AU - Rotinyan, T. A.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - apparent singular point

KW - Heun-class equation

KW - Painlevé equation

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