Application of unspecified sequences in symbolic summation

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn 2006, Issue , 2006, Pages 177-183

  Kauers, Manuel ^a   Schneider, Carsten ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Difference Fields; Symbolic Summation

Indexed keywords

AUTOMATION; COMPUTATIONAL METHODS; NUMERICAL METHODS; PROBLEM SOLVING;

DIFFERENCE FIELDS; SUMMATION TECHNOLOGY; SYMBOLIC SUMMATIONS;

DIFFERENTIAL EQUATIONS;

EID: 33748984412     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1145768.1145800     Document Type: Conference Paper

References (27)

1. S. Abramov, J. Carette, K. Geddes, and H. Le. Telescoping in the context of symbolic summation in Maple. Journal of Symbolic Computation, 38(4): 1303-1326, 2004.
2. S. A. Abramov. On the summability of p-recursive sequences. In this volume, 2006.
3. S. A. Abramov and M. Petkovšek. D'Alembertian solutions of linear differential and difference equations. In J. von zur Gathen, editor, Proc. ISSAC'94, pages 169-174. ACM Press, Baltimore, 1994.
4. S. A. Abramov and M. Petkovšek. Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula. In Proceedings of ISSAC'06, pages 5-12, 2005.
5. M. Bronstein. On solutions of linear ordinary difference equations in their coefficient field. J. Symbolic Comput., 29(6):841-877, June 2000.
6. R. M. Cohn. Difference Algebra. Interscience Publishers, John Wiley & Sons, 1965.
7. L. Comtet. Advanced Combinatorics. D. Reidel Publishing Company, 1970.
8. G. P. Egorychev. Integral Representation and the Computation of Combinatorial Sums. Translations of Mathematical Monographs. American Mathematical Society, Providence, RI, 1984. Translated from the Russian by H. H. McFadden. Translation edited by Lev J. Leifman.
9. W. Gosper. Decision procedure for indefinite hypergeometric summation. Proceedings of the National Academy of Sciences of the United States of America, 75:40-42, 1978.
10. M. Karr. Summation in finite terms. J. ACM, 28:305-350, 1981.
11. M. Kauers. Computer proofs for polynomial identities in arbitrary many variables. In Proceedings of ISSAC '04, pages 199-204, July 2004.
12. M. Kauers and C. Schneider. Indefinite summation with unspecified sequences. Discrete Mathematics, to appear.
13. P. Kirschenhofer. A note on alternating sums. Electron. J. Combin., 3(2), 1996.
14. D. Knuth. The art of computer programming, volume 1, Fundamental Algorithms. Addison Wesley, Reading, MA, 3rd edition, 2000.
15. P. Larcombe, M. Larsen, and E. Fennessey. On two classes of identities involving harmonic numbers. Util. Math., 67:65-80, 2005.
16. P. Paule. Greatest factorial factorization and symbolic summation. J. Symbolic Comput., 20:235-268, 1995.
17. P. Paule and C. Schneider. Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math., 31(2):359-378, 2003.
18. P. Paule and M. Schorn. A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities. Journal of Symbolic Computation, 20(5-6):673-698, 1995.
19. M. Petkovšek, H. S. Wilf, and D. Zeilberger. A = B. A. K. Peters, Wellesley, MA, 1996.
20. C. Schneider. Symbolic summation in difference fields. Technical Report 01-17, RISC-Linz, J. Kepler University, 2001. PhD Thesis.
21. C. Schneider. A collection of denominator bounds to solve parameterized linear difference equations in IIΣ-extensions. In D. P. et.al., editor, Proc. SYNASC04, 6th Internat. Symposium on Symbolic and Numeric Algorithms for Scientific Computation, pages 269-282. Mirton Publishing, 2004.
22. C. Schneider. The summation package Sigma: Underlying principles and a rhombus tiling application. Discrete Math. Theor. Comput. Sci., 6(2):365-386, 2004.
23. C. Schneider. Degree bounds to find polynomial solutions of parameterized linear difference equations in IIΣ-fields. Appl. Algebra Engrg. Comm. Comput., 16(1):l-32, 2005.
24. C. Schneider. Finding telescopers with minimal depth for indefinite nested sum and product expressions. In M. Kauers, editor, Proc. ISSAC'05, pages 285-292. ACM, 2005.
25. C. Schneider. Solving parameterized linear difference equations in terms of indefinite nested sums and products. J. Differ. Equations Appl., 11(9):799-821, 2005.
26. D. Zeilberger. The method of creative telescoping. J. Symbolic Comput., 11:195-204, 1991.
27. Z. Zhang. A kind of binomial identity. Discrete Math., 196:291-298, 1999.