论文标题
在Le Roy类型的广义三参数Wright功能上
On a generalized three-parameter Wright function of the Le Roy type
论文作者
论文摘要
最近S. Gerhold和R. Garra-F。 Polito独立引入了与Mittag-Leffler家族的特殊功能有关的新功能。此功能是E. Le Roy在1895 - 1905年期间研究的函数的概括，该功能与有限的收敛半径有关的分析性延续问题的问题。在我们的意见中，我们获得了此特殊功能的两个积分表示，计算其拉普拉斯变换，确定该函数在负半轴上的渐近扩展（在整数的第三参数$γ$）上，并为负的第一个参数$α$提供了延续。数值计算说明了渐近结果。还提出了有关可能的进一步研究和开放问题的讨论。
Recently S. Gerhold and R. Garra-F. Polito independently introduced a new function related to the special functions of Mittag-Leffler family. This function is a generalization of the function studied by E. Le Roy in the period 1895-1905 in connection with the problem of analytic continuation of power series with a finite radius of convergence. In our note we obtain two integral representations of this special function, calculate its Laplace transform, determine an asymptotic expansion of this function on the negative semi-axis (in the case of an integer third parameter $γ$) and provide its continuation to the case of a negative first parameter $α$. An asymptotic result is illustrated by numerical calculations. Discussion on possible further studies and open questions are also presented.
