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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 1, Pages 43–50
DOI: https://doi.org/10.31857/S0044466923010155 (Mi zvmmf11494) 		 
General numerical methods

On the structure of solutions to the key Gosper equation in problems of symbolic summation

E. V. Zima

Wilfrid Laurier University, Waterloo, Canada
DOI: https://doi.org/10.31857/S0044466923010155
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.
Key words: Indefinite hypergeometric summation, accelerated Gosper’s algorithm, factorial polynomials, polynomial normal forms.
Received: 10.05.2022
Revised: 01.06.2022
Accepted: 10.09.2022
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 1, Pages 40–47
DOI: https://doi.org/10.1134/S0965542523010153
Bibliographic databases:
Document Type: Article
UDC: 519.161
Language: Russian
Citation: E. V. Zima, “On the structure of solutions to the key Gosper equation in problems of symbolic summation”, Zh. Vychisl. Mat. Mat. Fiz., 63:1 (2023), 43–50; Comput. Math. Math. Phys., 63:1 (2023), 40–47
Citation in format AMSBIB
\Bibitem{Zim23}
\by E.~V.~Zima
\paper On the structure of solutions to the key Gosper equation in problems of symbolic summation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 1
\pages 43--50
\mathnet{http://mi.mathnet.ru/zvmmf11494}
\crossref{https://doi.org/10.31857/S0044466923010155}
\elib{https://elibrary.ru/item.asp?id=50398523}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 1
\pages 40--47
\crossref{https://doi.org/10.1134/S0965542523010153}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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