论文标题
Mittag-Leffler函数的计算
The calculation of the Mittag-Leffler function
论文作者
论文摘要
在论文中考虑了计算Mittag-Leffler函数$ e_ {ρ，μ}（z）$的问题。为了解决该函数$ e_ {ρ，μ}（z）$的整体表示形式，以使它们无法包含复杂的变量和参数的方式进行转换。以这种形式编写的积分表示允许一个人使用标准的数值集成方法来计算它们中包含的积分。为了验证获得函数$ e_ {ρ，μ}（z）$的积分表示的正确性，这两者都使用获得的公式以及使用Mittag-Leffler函数的已知表示形式来计算。计算结果证明了它们的确切匹配。这一事实表明了获得的函数$ e_ {ρ，μ}（z）$的新积分表示的正确性。
The problem of calculating the Mittag-Leffler function $E_{ρ,μ} (z)$ is considered in the paper. To solve this problem integral representations for the function $E_{ρ,μ}(z)$ are transformed in such a way that they could not contain complex variables and parameters. Integral representations written in this form allow one to use standard methods of numerical integration to calculate integrals contained in them. To verify the correctness of the integral representations obtained the function $E_{ρ,μ}(z)$ was calculated both with the use of obtained formulas and with the use of known representations of the Mittag-Leffler function. The calculation results demonstrate their exact matching. This fact is indicative of the correctness of new integral representations of the function $E_{ρ,μ}(z)$ that were obtained.
