Degree bounds to find polynomial solutions of parameterized linear difference equations in Π∑-fields

Applicable Algebra in Engineering, Communications and Computing

Volumn 16, Issue 1, 2005, Pages 1-32

  Schneider, Carsten ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Fields; Degree Bounds; Linear Difference Equations

Indexed keywords

ALGEBRA; ALGORITHMS; LINEAR EQUATIONS; POLYNOMIALS; PROBLEM SOLVING;

ΠΣ-FIELDS; DEGREE BOUNDS; LINEAR DIFFERENCE EQUATIONS; MULTI-SUM IDENTITIES; NESTED MULTISUM EXPRESSIONS;

DIFFERENCE EQUATIONS;

EID: 15844414168     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00200-004-0167-3     Document Type: Article

References (26)

1. Abramov, S.A.: Problems in computer algebra that are connected with a search for polynomial solutions of linear differential and difference equations. Moscow Univ. Comput. Math. Cybernet. 3, 63-68 (1989)
2. Abramov, S.A.: Rational solutions of linear differential and difference equations with polynomial coefficients. U.S.S.R. Comput. Math. Math. Phys. 29(6), 7-12 (1989)
3. Abramov, S.A.: Rational solutions of linear difference and q-difference equations with polynomial coefficients. In: T. Levelt, (ed.), Proc. ISSAC'95, ACM Press, New York, 1995, pp. 285-289
4. Abramov, S.A., Bronstein, M., Petkovšek, M.: On polynomial solutions of linear operator equations. In: T. Levelt, (ed.), Proc. ISSAC'95, ACM Press, New York, 1995, pp. 290-296
5. Andrews, G.E., Paule, P., Schneider, C.: Plane partitions VI: Stembridge's TSPP Theorem. To appear in the Dave Robbins memorial issue of Advances in Applied Math., 2005
6. Bronstein, M.: On solutions of linear ordinary difference equations in their coefficient field. J. Symbolic Comput. 29(6), 841-877 June 2000
7. Chyzak, F.: An extension of Zeilberger's fast algorithm to general holonomic functions. Discrete Math. 217, 115-134 (2000)
8. Cohn, R.M.: Difference Algebra. Interscience Publishers, John Wiley & Sons, 1965
9. Driver, K., Prodinger, H., Schneider, C., Weideman, A.: Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation. To appear in Ramanujan Journal, 2005
10. Driver, K., Prodinger, H., Schneider, C., Weideman, A.: Padé approximations to the logarithm III: Alternative methods and additional results. To appear in Ramanujan Journal, 2005
11. Karr, M.: Summation in finite terms. J. ACM 28, 305-350 (1981)
12. Karr, M.: Theory of summation in finite terms. J. Symbolic Comput. 1, 303-315 (1985)
13. Paule, F., Schneider, C.: Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math. 31(2), 359-378 (2003)
14. Petkovšek, M.: Hypergeometric solutions of linear recurrences with polynomial coefficients. J. Symbolic Comput. 14(2-3), 243-264 (1992)
15. Petkovšek, M., Weixlbaumer, C.: A comparison of degree polynomials, http://www.fmf.uni-lj.si/~petkovsek/, 2000, Note
16. Petkovšek, M., Wilf, H.S., Zeilberger, D.: A = B. A. K. Peters, Wellesley, MA, 1996
17. Schneider, C.: An implementation of Karr's summation algorithm in Mathematica. Sém. Lothar. Combin. S43b, 1-10 (2000)
18. Schneider, C.: Symbolic summation in difference fields. Technical Report 01-17, RISC-Linz, J. Kepler University, 2001, PhD Thesis
19. Schneider, C.: Solving parameterized linear difference equations in ∏ Σ-fields. SFB-Report 02-19, J. Kepler University, Linz, November 2002, Submitted
20. Schneider, C.: A collection of denominator bounds to solve parameterized linear difference equations in ∏ Σ-extensions. In: D. Petcu, V. Negru, D. Zaharie, T. Jebelean, (eds.), Proc. SYNASC04, 6th Internat. Symposium on Symbolic and Numeric Algorithms for Scientific Computation, Timisoara (Romania), September 2004. Mirton Publishing. ISBN 973-661-441-7, pp. 269-282
21. Schneider, C.: A new Sigma approach to multi-summation. To appear in the Dave Robbins memorial issue of Advances in Applied Math. 2005
22. C. Schneider. Product representations in ∏ Σ-fields. Annals of Combinatorics 9(1), 75-99 (2005)
23. C. Schneider. The summation package Sigma: Underlying principles and a rhombus tiling application. Discrete Math. Theor. Comput. Sci. 6(2), 365-386 (2004)
24. Schneider, C.: Symbolic summation with single-nested sum extensions. In: J. Gutierrez, (ed.) Proc. ISSAC'04, ACM Press, 2004, pp. 282-289
25. van Hoeij, M.: Rational solutions of linear difference equations. In: O. Gloor, (ed.), Proc. ISSAC'98, ACM Press, 1998, pp. 120-123
26. Zeilberger, D.: A fast algorithm for proving terminating hypergeometric identities. Discrete Math. 80(2), 207-211 (1990)