# Apparent singularities of linear difference equations with polynomial coefficients

@article{Abramov2005ApparentSO, title={Apparent singularities of linear difference equations with polynomial coefficients}, author={S. Abramov and M. Barkatou and M. V. Hoeij}, journal={Applicable Algebra in Engineering, Communication and Computing}, year={2005}, volume={17}, pages={117-133} }

Let L be a linear difference operator with polynomial coefficients. We consider singularities of L that correspond to roots of the trailing (resp. leading) coefficient of L. We prove that one can effectively construct a left multiple with polynomial coefficients of L such that every singularity of is a singularity of L that is not apparent. As a consequence, if all singularities of L are apparent, then L has a left multiple whose trailing and leading coefficients equal 1.

#### Topics from this paper

34 Citations

Removing Apparent Singularities of Systems of Linear Differential Equations with Rational Function Coefficients

- Mathematics, Computer Science
- ISSAC
- 2015

12

Removing apparent singularities of linear difference systems

- Mathematics, Computer Science
- J. Symb. Comput.
- 2021

Desingularization of First Order Linear Difference Systems with Rational Function Coefficients

- Mathematics, Computer Science
- ISSAC
- 2018

2- PDF

Analytic Solutions of Linear Difference Equations, Formal Series, and Bottom Summation

- Mathematics, Computer Science
- CASC
- 2007

2- PDF

D'Alembertian series solutions at ordinary points of LODE with polynomial coefficients

- Computer Science, Mathematics
- J. Symb. Comput.
- 2009

2- PDF

#### References

SHOWING 1-10 OF 17 REFERENCES

Set of poles of solutions of linear difference equations with polynomial coefficients

- Mathematics
- 2003

8

On the Relation between Linear Difference and Differential Equations with Polynomial Coefficients

- Mathematics
- 1999

5- PDF

Formal Solutions and Factorization of Differential Operators with Power Series Coefficients

- Computer Science, Mathematics
- J. Symb. Comput.
- 1997

62- PDF

Weyl Closure of a Linear Differential Operator

- Computer Science, Mathematics
- J. Symb. Comput.
- 2000

33 Highly Influential- PDF

Rational solutions of linear difference and q-difference equations with polynomial coefficients

- Mathematics, Computer Science
- ISSAC '95
- 1995

110

Fast polynomial dispersion computation and its application to indefinite summation

- Mathematics, Computer Science
- ISSAC '94
- 1994

31

Desingularization of linear difference operators with polynomial coefficients

- Mathematics, Computer Science
- ISSAC '99
- 1999

18

Hypergeometric Solutions of Linear Recurrences with Polynomial Coefficents

- Computer Science, Mathematics
- J. Symb. Comput.
- 1992

256- PDF