The Cauchy problem for multidimensional difference equations in lattice cones
Alexander P. Lyapinab, Sreelatha Chandragirib
a Lesosibirsk Pedagogical Institute — branch of SFU,
Lesosibirsk, Russian Federation
b Siberian Federal University, Krasnoyarsk, Russian Federation
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.
difference equation, fundamental solution, generating function, Dyck paths.
|This work of author was financed by the PhD SibFU grant for support of scientific research no. 14.
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Received in revised form: 26.01.2020
Alexander P. Lyapin, Sreelatha Chandragiri, “The Cauchy problem for multidimensional difference equations in lattice cones”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 187–196
Citation in format AMSBIB
\by Alexander~P.~Lyapin, Sreelatha~Chandragiri
\paper The Cauchy problem for multidimensional difference equations in lattice cones
\jour J. Sib. Fed. Univ. Math. Phys.
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