标题： 矩展开方程的解 显示英文标题

标题： Solution to the Equations of the Moment Expansions

摘要： 我们开发了一个公式，用于匹配关于原点的泰勒级数和坐标大值时的渐近指数展开。 我们在哈密顿算符的矩生成函数的展开中测试了它。 在前一种情况下，该公式在Krylov空间中为Rayleigh-Ritz方法产生了能量和重叠。 我们选择简谐振子和强非简谐振子作为数值测试的示例。 我们的结果揭示了连通矩展开的一些特性，这些特性在早期的研究和应用中被忽略了。 显示英文摘要

摘要： We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach.