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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2023 Volume 63, Number 1, Pages 43–50 (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

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.

UDC: 519.161

Received: 10.05.2022
Revised: 01.06.2022
Accepted: 10.09.2022

DOI: 10.31857/S0044466923010155


 English version:
Computational Mathematics and Mathematical Physics, 2023, 63:1, 40–47

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© Steklov Math. Inst. of RAS, 2026