Full asymptotic expansions of the Landau constants via a difference equation approach
Full asymptotic expansions of the Landau constants via a difference equation approach
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DOI：
10.1016/j.amc.2012.07.003
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发表时间：
2012-10
期刊：
影响因子：
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通讯作者：
Yutian Li;Saiyu Liu;Shuai‐Xia Xu;Yuqiu Zhao
中科院分区：
文献类型：
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作者：
Yutian Li;Saiyu Liu;Shuai‐Xia Xu;Yuqiu Zhao
我们得到了朗道常数Gnas n→∞的完全渐近展开式。一些扩展并不是新的，但所有的系数的扩展迭代地给出了一个明确的方式，并更有效地评估与已知的结果。应用Wong和Li的理论，得到了二阶线性差分方程的新老渐近公式。在推导展开式的过程中，我们还证实了尼弥斯和尼弥斯的一个猜想。
We derive full asymptotic expansions for the Landau constants Gnas n→∞. Some of the expansions are not new, yet all the coefficients of the expansions are given iteratively in an explicit manner, and are more efficiently evaluated as compared with the known results. We obtain the asymptotic formulas, old and new, by applying the theory of Wong and Li for second-order linear difference equations. In deriving the expansions, we have also confirmed a conjecture made by Nemes and Nemes.