大变量指数的求取方法
Methods of Retrieving Large-Variable Exponents
摘要：
方法确定，从小变量渐近展开式，变量趋于无穷大的特征指数进行了分析。考虑了以下方法：diff-log Padé求和、自相似因子近似、自相似diff-log求和、自相似Borel求和和自相似Borel-Leroy求和。处理了几个典型问题。结果比较表明，所有这些方法提供了接近的估计的大变量指数。当不同求和方法相容时，得到了可靠的估计。
英文摘要：
Methods of determining, from small-variable asymptotic expansions, the characteristic exponents for variables tending to infinity are analyzed. The following methods are considered: diff-log Padé summation, self-similar factor approximation, self-similar diff-log summation, self-similar Borel summation, and self-similar Borel-Leroy summation. Several typical problems are treated. The comparison of the results shows that all these methods provide close estimates for the large-variable exponents. The reliable estimates are obtained when different methods of summation are compatible with each other.
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