An attempt is made here to study the Mittag–Leffler function with two variables. Its various properties including integral and operational relationships with other known Mittag–Leffler functions of one variable, pure and differential recurrence relations, Euler transform, Laplace transform, Mellin transform, Whittaker transform, Mellin–Barnes integral representation, and its relationship with Wright hypergeometric function are investigated and established. Also, properties of the Mittag–Leffler function of two variables associated with fractional calculus operators are considered.

中文翻译：

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与两个变量的 Mittag-Leffler 函数有关的一些性质

这里尝试研究具有两个变量的 Mittag-Leffler 函数。它的各种性质，包括与其他已知的单变量米塔格-莱弗勒函数的积分和运算关系、纯和微分递归关系、欧拉变换、拉普拉斯变换、梅林变换、惠特克变换、梅林-巴恩斯积分表示，以及它与赖特超几何函数的关系被调查并成立。此外，还考虑了与分数运算运算符相关的两个变量的 Mittag-Leffler 函数的性质。