论文标题
指数泰勒系列
Exponential Taylor Series
论文作者
论文摘要
本文得出了一种表达可区分的复杂值函数作为$（1-e^{λx}）$的功率之和的方法，其中$λ\ in \ mathbb {r} $，其余的公式为剩余的公式。然后，该公式用于将无限系列与$ c^\ infty $函数相关联，该功能显示出在剩余的适当条件下恢复原始功能。这些结果还用于计算一些涉及斯特林数字的无限序列，并提供了一些示例。
This paper derives a way to express differentiable complex-valued functions as the sum of powers of $(1-e^{λx})$, where $λ\in\mathbb{R}$, with an explicit formula for the remainder. This formulation is then used to associate an infinite series to $C^\infty$ functions, which is shown to recover the original function under suitable conditions on the remainder. These results are also used to calculate some infinite series involving Stirling Numbers, as well as providing a few examples.
