An asymptotic formula for solutions of linear second-order difference equations with regularly behaving coefficients
An asymptotic formula for solutions of linear second-order difference equations with regularly behaving coefficients
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DOI：
10.1080/10236190701414462
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发表时间：
2007-10
影响因子：
1.1
通讯作者：
R. Kooman
中科院分区：
文献类型：
--
作者：
R. Kooman
给出了一类二阶线性差分方程解的渐近公式，它在系数为正则的情况下成立，特别是当系数为指数n的幂的级数时，该公式也成立，并给出了xn和的最低阶渐近性质.给出的算例表明，对系数性态的条件不能削弱太多。该方法使用了矩阵序列，可以推广到其他情况。
An asymptotic formula is given for the solutions of a linear second-order difference equation which holds in the case that the coefficients exhibit regular behaviour; in particular, the formula holds in the case that the coefficients are series of powers of the index n. The lowest order asymptotic behaviour is given for both x n and . Examples are given that show that the conditions on the behaviour of the coefficients cannot be weakened too much. The method presented here, which uses matrix sequences, can be extended to other cases.