M. S. Sgibnev, “Exact asymptotics of the solution to a difference equation of general type”, Sib. J. Pure and Appl. Math., 2017, Volume 17, Issue 1,Pages <nobr>45

Exact asymptotics of the solution to a difference equation of general type

M. S. Sgibnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: An asymptotic expansion for the solution to a nonhomogeneous difference equation of general type is obtained. The influence of the roots of the characteristic equation is taken into account. The asymptotic behavior of the remainder is established, depending on the asymptotics of the nonhomogeneous term of the equation.

Keywords: numbering, Rogers semilattice, hyperarithmetical hierarchy, minimal elements, minimal covers.

UDC: 517.965

Received: 14.10.2015

DOI: 10.17377/PAM.2017.17.104