This article is cited in 7 papers

The Cauchy problem for multidimensional difference equations in lattice cones

Alexander P. Lyapin^ab, Sreelatha Chandragiri<sup>b

a</sup> Lesosibirsk Pedagogical Institute — branch of SFU, Lesosibirsk, Russian Federation
^b Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: We consider a variant of the Cauchy problem for a multidimensional difference equation with constant coefficients, which connected with a lattice path problem in enumerative combinatorial analysis. We obtained a formula in which generating function of the solution to the Cauchy problem is expressed in terms of generating functions of the Cauchy data and a formula expressing solution to the Cauchy problem through its fundamental solution and Cauchy data.

Keywords: difference equation, fundamental solution, generating function, Dyck paths.

UDC: 517.55+517.962.26

Received: 21.12.2019
Received in revised form: 26.01.2020
Accepted: 03.02.2020

Language: English

DOI: 10.17516/1997-1397-2020-13-2-187-196

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