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- W1996740555 abstract "It is shown that if the zeros ${lambda _1},{lambda _2}, ldots ,{lambda _n}$ of the polynomial [ q(lambda ) = {lambda ^n} + {a_1}{lambda ^{n - 1}} + cdots + {a_n}] are distinct and $r$ is an integer in ${ 1,2, ldots ,n}$ such that $|{lambda _s}| ne |{lambda _r}|$ if $s ne r$, then the Poincaré difference equation [ y(n + m) + ({a_1} + {p_1}(m))y(n + m - 1) + cdots + ({a_n} + {p_n}(m))y(m) = 0] has a solution ${y_r}$ such that (A) ${y_r}(m) = lambda _r^m(1 + o(1))$ as $m to infty$, provided that the sums $sum nolimits _{j = m}^infty {{p_i}(j);(1 leqslant i leqslant n)}$ converge sufficiently rapidly. Our results improve over previous results in that these series may converge conditionally, and we give sharper estimates of the $o(1)$ terms in (A)." @default.
- W1996740555 created "2016-06-24" @default.
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- W1996740555 date "1993-02-01" @default.
- W1996740555 modified "2023-10-18" @default.
- W1996740555 title "Asymptotic behavior of solutions of Poincaré difference equations" @default.
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- W1996740555 doi "https://doi.org/10.1090/s0002-9939-1993-1184088-5" @default.
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