由局部展开式整体重构解析函数
Global reconstruction of analytic functions from local expansions
摘要：
本文提出了一种新的求和方法，将一类较广的无穷和局部展开式转化为积分。的整表示产量的全球信息，如解析连续性，位置的奇点，渐近大值的变量和渐近位置的零点。重构函数的全局解析结构与系数作为其指数的函数的性质之间存在对偶性。作为一个副产品，给出了一类发散级数的Borel可和性.
英文摘要：
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities, asymptotics for large values of the variable and asymptotic location of zeros. There is a duality between the global analytic structure of the reconstructed function and the properties of the coefficients as a function of their index. Borel summability of a class of divergent series follow as a byproduct.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
