论文标题
Mittag-Leffler功能的积分表示的单数点
Singular points of the integral representation of the Mittag-Leffler function
论文作者
论文摘要
本文介绍了两参数Mittag-Leffler函数$ e_ {ρ，μ}（z）$的整体表示，并且已经研究了该表示的单数点。已经发现，此积分表示有两个单数：$ζ= 1 $和$ζ= 0 $。点$ζ= 1 $是第一阶的极点，而点$ζ= 0 $，具体取决于参数的值$ρ，μ$是极点或分支点或常规点。随后的研究表明，在某些值的值下，$ρ，μ$借助残基理论，可以计算研究的积分表示中包含的积分，并通过基本函数表达函数$ e_ {ρ，μ}（z）$。
The paper presents an integral representation of the two-parameter Mittag-Leffler function $E_{ρ,μ}(z)$ and singular points of this representation have been studied. It has been found that there are two singular points for this integral representation: $ζ=1$ and $ζ=0$. The point $ζ=1$ is a pole of the first order and the point $ζ=0$, depending on the values of parameters $ρ,μ$ is either a pole or a branch point, or a regular point. The subsequent study showed that at some values of parameters $ρ,μ$ with the help of the residue theory one can calculate the integral included in the studied integral representation and express the function $E_{ρ,μ}(z)$ through elementary functions.
