On the Structure of Solutions to the Key Gosper Equation in Problems of Symbolic Summation
- Authors: Zima E.V.1
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Affiliations:
- Wilfrid Laurier University
- Issue: Vol 63, No 1 (2023)
- Pages: 43-50
- Section: ОБЩИЕ ЧИСЛЕННЫЕ МЕТОДЫ
- URL: https://journals.rcsi.science/0044-4669/article/view/134286
- DOI: https://doi.org/10.31857/S0044466923010155
- EDN: https://elibrary.ru/LEDEOY
- ID: 134286
Cite item
Abstract
The structure of polynomial solutions to the Gosper’s key equation is analyzed. A method for rapid “extraction” of simple high-degree factors of the solution is given. It is shown that in cases when equation corresponds to a summable non-rational hypergeometric term the Gosper’s algorithm can be accelerated by removing non-essential dependency of its running time on the value of dispersion of its rational certificate.
About the authors
E. V. Zima
Wilfrid Laurier University
Author for correspondence.
Email: ezima@wlu.ca
Waterloo, Canada
References
- Абрамов С.А. О суммировании рациональных функций // Ж. вычисл. матем. и матем. физ. 1971. Т. 11. № 4. С. 1071–1075.
- Gosper R.W., Jr. Decision procedure for indefinite hypergeometric summation // Proc. Nat. Acad. Sci. U.S.A., 75(1):40–42, 1978.
- Abramov S.A., Petkovšek M. Rational normal forms and minimal decompositions of hypergeometric terms // J. of Symbolic Computation, 33(5):521–543, 2002.
- Maple User Manual. Maplesoft, a division of Waterloo Maple Inc., 1996–2021.
- Абрамов С.А. Элементы компьютерной алгебры линейных обыкновенных дифференциальных, разностных и q-разностных операторов. М: МЦМНО, 2012.
- Moenck R. On computing closed forms for summations // In Proc. of the 1977 MACSYMA Users’ Conference, pp. 225–236, 1977.
- Petkovšek M. Hypergeometric solutions of linear recurrences with polynomial coefficients // J. of Symbolic C-omputation, 14(2):243–264, 1992.
- Lisonek P., Paule P., Strehl V. Improvement of the degree setting in Gosper’s algorithm // J. of Symbolic Computation, 16 (1993), 243–258.
- Pirastu R., Strehl V. Rational summation and Gosper-Petkovsšek representation // J. Symb. Comput., 20(5‑6):617–635, Nov. 1995.
- Zima E.V. Accelerating indefinite hypergeometric summation algorithms // ACM Commun. Comput. Algebra, 52(3):96–99, 2019.