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JOURNALS // Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki // Archive

Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2021 Volume 31, Issue 3, Pages 414–423 (Mi vuu778)

This article is cited in 2 papers

MATHEMATICS

Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation

A. P. Lyapina, S. S. Akhtamovab

a Siberian Federal University, pr. Svobodnyi, 79, Krasnoyarsk, 660041, Russia
b Lesosibirsk Pedagogical Institute — Branch of SibFU, ul. Pobedy, 42, Lesosibirsk, Krasnoyarskii Krai, 662544, Russia

Abstract: In this paper, we study the sections of the generating series for solutions to a linear multidimensional difference equation with constant coefficients and find recurrent relations for these sections. As a consequence, a multidimensional analogue of Moivre's theorem on the rationality of sections of the generating series depending on the form of the initial data of the Cauchy problem for a multidimensional difference equation is proved. For problems on the number of paths on an integer lattice, it is shown that the sections of their generating series represent the well-known sequences of polynomials (Fibonacci, Pell, etc.) with a suitable choice of steps.

Keywords: difference equation, generating function, section, lattice path.

UDC: 517.55

MSC: 32A05, 32A08, 39B32, 05A15

Received: 09.03.2021

DOI: 10.35634/vm210305



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