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Home » Issues » Archive of Issues » 2021 - 3 issue » pp. 414-423

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Russia Krasnoyarsk; Lesosibirsk
Year
2021
Volume
31
Issue
3
Pages
414-423
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Section Mathematics
Title Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation
Author(-s) Lyapin A.P.a, Akhtamova S.S.b
Affiliations Siberian Federal Universitya, Lesosibirsk Pedagogical Institute — Branch of Siberian Federal Universityb
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
DOI 10.35634/vm210305
Received 9 March 2021
Language Russian
Citation Lyapin A.P., Akhtamova S.S. Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 3, pp. 414-423.
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