Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation
A. P. Lyapin, Svetlana S. Akhtamova
2021Vestnik Udmurtskogo Universiteta Matematika Mekhanika Komp yuternye Nauki14 citationsDOIOpen Access PDF
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.
Topics & Concepts
Fibonacci numberRecurrence relationMathematicsSeries (stratigraphy)Integer (computer science)RationalityLattice (music)Pure mathematicsCombinatoricsMathematical analysisComputer scienceProgramming languageBiologyPaleontologyAcousticsPolitical scienceLawPhysicsadvanced mathematical theoriesAdvanced Computational Techniques in Science and EngineeringCoding theory and cryptography