# Integral representations and asymptotic behaviours of Mittag-Leffler type functions of two variables

## TL;DR

This paper investigates generalized two-variable Mittag-Leffler functions, deriving integral representations and asymptotic behaviors, thereby expanding understanding of their properties for large variable values.

## Contribution

It provides new integral representations and asymptotic formulas for generalized Mittag-Leffler functions of two variables, enhancing theoretical understanding.

## Key findings

- Derived integral representations in various domains.
- Established asymptotic expansion formulas.
- Proved properties of these functions for large variables.

## Abstract

The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values of the parameters are obtained. The asymptotic expansions formulas and asymptotic properties of such functions are also established for large values of the variables. This provides statements of theorems for these formulas and their corresponding properties.