Email this article 
POLYNOMIAL RELATIONS FOR BOUNDS ON THE EXPONENTS IN SOLUTIONS TO OPERATOR EQUATIONS
- Authors: Abramov S.A.1, Ryabenko A.A.1
-
Affiliations:
- Federal Research Center “Computer Science and Control” of Russian Academy of Sciences
- Issue: No 1 (2025)
- Pages: 51-58
- Section: COMPUTER ALGEBRA
- URL: https://ogarev-online.ru/0132-3474/article/view/287079
- DOI: https://doi.org/10.31857/S0132347425010066
- EDN: https://elibrary.ru/DXFWOP
- ID: 287079
Cite item
Open Access
Access granted
Subscription Access
Abstract
A general approach to finding the indicial polynomials for differential, difference, and q-difference operators is discussed. The structure of such a polynomial corresponding to the product of operators is considered.
About the authors
S. A. Abramov
Federal Research Center “Computer Science and Control” of Russian Academy of Sciences
Email: sergeyabramov@mail.ru
Moscow, Russia
A. A. Ryabenko
Federal Research Center “Computer Science and Control” of Russian Academy of Sciences
Email: anna.ryabenko@gmail.com
Moscow, Russia
References
- Abramov S.A. On the multiplicative property of indicial polynomials // Comput. Math. Math. Phys. (in press)
- Coddington E.A., Levinson N. Theory of Ordinary Differential Equations. New York: McGraw-Hill, 1955
- Davenport J., Siret Y., Tournier E. Calcul formel. Paris: Masson, 1987
- Abramov S.A. Problems of computer algebra involved in the search for polynomial solutions of linear differential and difference equations // Moscow Univ. Comput. Math. and Cybernet, 1989, no. 3, pp. 63–68
- Petkovsek M. Finding closed-form solutions of difference equations by symbolic methods. Ph.D. Dissertation. Carnegie Mellon University, USA. Order Number: UMI Order No. GAX91-33361. 1991.
- Abramov S.A. Elements of Computer Algebra and Linear Ordinary Differential, Difference, and Difference Operators, Moscow: Mosk. Tsentr Nepreryvnogo Mat. Obrazovaniya, 2012 [in Russian].
- Abramov S., Bronstein M., Petkovsek M. On polynomial solutions of linear operator equations // ISSAC’95 Proceedings. 1995. P. 290–295.
- Abramov S., Petkovsek M., Ryabenko A. Special formal series solutions of linear operator equations // Discrete Math. 2000. V. 210. P. 3–25.
- Khmelnov D.E. Basis selection in solving linear functional equations // Program. Comput. Software, 2002, vol. 28, no. 2. pp. 102–105.
- Khmelnov D.E. Search for polynomial solutions of linear functional systems by means of induced recurrences // Program. Comput. Software, 2004, vol. 30, no. 2, pp. 61–67.
Supplementary files
