# 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.

## 11 Citations

### Symmetries and apparent singularities for the simplest Fuchsian equations

- Mathematics
- 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…

### Symmetries and apparent singularities for the simplest Fuchsian equations

- MathematicsTheoretical 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…

### Relations Between Second-Order Fuchsian Equations and First-Order Fuchsian Systems

- MathematicsJournal of Mathematical Sciences
- 2019

Each component of any solution of a Fuchsian differential system satisfies a Fuchsian differential equation. The set of Fuchsian systems is fibered into equivalence classes. Each class consists of…

### Generalized Hypergeometric Solutions of the Heun Equation

- MathematicsTheoretical and Mathematical Physics
- 2020

We present infinitely many solutions of the general Heun equation in terms of generalized hypergeometric functions. Each solution assumes that two restrictions are imposed on the involved parameters:…

### Generalized Hypergeometric Solutions of the Heun Equation

- MathematicsTheoretical and Mathematical Physics
- 2020

We present infinitely many solutions of the general Heun equation in terms of generalized hypergeometric functions. Each solution assumes that two restrictions are imposed on the involved parameters:…

### Confluent Heun Equation and Confluent Hypergeometric Equation

- Mathematics, PhysicsJournal of Mathematical Sciences
- 2018

The confluent Heun equation and the confluent hypergeometric equation are studied in scalar and vector forms with particular emphasis on the role of apparent singularities. A relation to the Painlevé…

### Antiquantization, isomonodromy, and integrability

- MathematicsJournal of Mathematical Physics
- 2018

An extended analysis of links between linear differential equations and the nonlinear Painleve equation PV I is given. For linear equations, second-order equations in different forms, as well as…

### From Heun Class Equations to Painlevé Equations

- Mathematics
- 2020

In the first part of our paper we discuss linear 2nd order differential equations in the complex domain, especially Heun class equations, that is, the Heun equation and its confluent cases. The…

### Kinetic analysis of pore formation in die-cast metals and influence of absolute pressure on porosity

- Materials ScienceVacuum
- 2019

### Relations Between Second-Order Fuchsian Equations and First-Order Fuchsian Systems

- MathematicsJournal of Mathematical Sciences
- 2019

Each component of any solution of a Fuchsian differential system satisfies a Fuchsian differential equation. The set of Fuchsian systems is fibered into equivalence classes. Each class consists of…

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