Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation
2021 ◽
Vol 31
(3)
◽
pp. 414-423
Keyword(s):
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.
2020 ◽
pp. 187-196
2017 ◽
Vol 43
(2)
◽
pp. 105-111
◽
2020 ◽
Vol 10
(1)
◽
pp. 353-370
◽
Keyword(s):
2021 ◽
Vol 18
(03)
◽
pp. 701-728
1983 ◽
Vol 94
(1-2)
◽
pp. 137-147
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