论文标题
Mittag-Leffler函数的两种形式的积分表示
Two forms of the integral representations of the Mittag-Leffler function
论文作者
论文摘要
两参数Mittag-Leffler函数的积分表示$ e_ {ρ，μ}（z）$在论文中考虑以轮廓积分表示其值。对于此积分表示，该过渡是通过集成在复杂变量到实际变量集成的。结果表明，由于这种过渡的结果，函数的积分表示$ e_ {ρ，μ}（z）$具有两种形式：表示``a''''''''''''''''''''''''''''''''''''和`这些表示中的每一个都有其优点和缺点。在本文中，对相应的定理进行了制定和证明，并讨论了每个获得的表示的优势和缺点。
The integral representation of the two-parameter Mittag-Leffler function $E_{ρ,μ}(z)$ is considered in the paper that expresses its value in terms of the contour integral. For this integral representation, the transition is made from integration over a complex variable to integration over real variables. It is shown that as a result of such a transition, the integral representation of the function $E_{ρ,μ}(z)$ has two forms: the representation ``A'' and ``B''. Each of these representations has its advantages and drawbacks. In the paper, the corresponding theorems are formulated and proved, and the advantages and disadvantages of each of the obtained representations are discussed.
