论文标题
在持续扩展特殊函数的分数和持续分数收敛的明确表达
On a continued fraction expansion of the special function and an explicit expression of the continued fraction convergents
论文作者
论文摘要
在本文中，我们定义了“无穷大的指数积分$ e_ {1}（x）$的持续分数扩展”，这类似于定期持续的实际数字分数扩展，并证明这种扩展给出了相同的持续分数。此外，我们提供了通过截断持续分数获得的理性功能的具体表示。
In this paper we define "a continued fraction expansion of the exponential integral $E_{1}(x)$ at infinity", which is analogous to the regular continued fraction expansion of real numbers, and prove that this expansion gives the same continued fraction. Moreover, we give concrete representations of rational functions which are obtained by truncating the continued fraction.
