ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2022. Vol 42

Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone

Alexander P. Lyapin1,2, Tom Cuchta2

1Siberian Federal University, Krasnoyarsk, Russian Federation

2Fairmont State University, Fairmont, West Virginia, USA

We consider a multidimensional difference equation in a simplicial lattice cone with coefficients from a field of characteristic zero and sections of a generating series of a solution to the Cauchy problem for such equations. We use properties of the shift and projection operators on the integer lattice Z𝑛 to find a recurrence relation (difference equation with polynomial coefficients) for the section of the generating series. This formula allows us to find a generating series of a solution to the Cauchy problem in the lattice cone through a generating series of its initial data and a right-side function of the difference equation. We derived an integral representation for sections of the holomorphic function, whose coefficients satisfy the difference equation with complex coefficients. Finally, we propose a system of differential equations for sections that represent D-finite functions of two complex variables.
About the Authors

Alexander P. Lyapin, Cand. Sci. (Phys.–Math.), Assoc. Prof., Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, aplyapin@sfu-kras.ru

Tom Cuchta, PhD, Assist. Prof., Fairmont State University, Fairmont, WV, 26554, USA, tcuchta@fairmontstate.edu

For citation
Lyapin A. P., Cuchta T. Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 42, pp. 75–89. https://doi.org/10.26516/1997-7670.2022.42.75
generating series, difference equation, lattice cone, Stanley hierarchy, section
39A06, 32A10, 39A10, 39A14
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