标题： 关于超几何和梅塔格-莱夫勒函数混合族的模糊见解 显示英文标题

标题： Umbral insights into a hybrid family of hypergeometric and Mittag-Leffler functions

摘要： 幕影方法提供了理解与重新定义特殊函数的方法。 该方法被有效用于揭示复杂性并引入新的特殊函数族。 在本文中，采用幕影视角来介绍一种超几何函数和Mittag-Leffler函数的混合族。 幕影运算过程用于推导生成函数、显式表示、微分递推公式和特定积分公式。 此外，建立了超几何-Mittag-Leffler函数的拉普拉斯变换和Sumudu变换。 还给出了参数适当值下的零点分布图形表示和模式。 显示英文摘要

摘要： The umbral approach provides methods for comprehending and redefining special functions. This approach is employed efficiently in order to uncover intricacies and introduce new families of special functions. In this article, the umbral perspective is adopted to introduce a hybrid family of hypergeometric and Mittag-Leffler functions. The umbral-operational procedures are used to derive the generating functions, explicit representations, differential recurrence formulae, and specific integral formulae. Further, the Laplace and Sumudu transforms for the hypergeometric-Mittag-Leffler functions are established. The graphical representation and pattern for distribution of zeros for suitable values of parameters are also presented.