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Siberian Journal of Pure and Applied Mathematics, 2017, Volume 17, Issue 1, Pages 45–54
DOI: https://doi.org/10.17377/PAM.2017.17.104 (Mi vngu429) 		 
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
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DOI: https://doi.org/10.17377/PAM.2017.17.104
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.
Received: 14.10.2015
English version:
Journal of Mathematical Sciences, 2018, Volume 231, Issue 2, Pages 267–277
DOI: https://doi.org/10.1007/s10958-018-3821-1
Document Type: Article
UDC: 517.965
Language: Russian
Citation: M. S. Sgibnev, “Exact asymptotics of the solution to a difference equation of general type”, Sib. J. Pure and Appl. Math., 17:1 (2017), 45–54; J. Math. Sci., 231:2 (2018), 267–277
Citation in format AMSBIB
\Bibitem{Sgi17}
\by M.~S.~Sgibnev
\paper Exact asymptotics of the solution to a difference equation of general type
\jour Sib. J. Pure and Appl. Math.
\yr 2017
\vol 17
\issue 1
\pages 45--54
\mathnet{http://mi.mathnet.ru/vngu429}
\crossref{https://doi.org/10.17377/PAM.2017.17.104}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 231
\issue 2
\pages 267--277
\crossref{https://doi.org/10.1007/s10958-018-3821-1}
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