Some New Results for Generalized Incomplete Exponential Matrix Functions

TL;DR

This paper introduces new generalized incomplete exponential matrix functions, explores their properties, and connects them with existing matrix functions like gamma and Bessel matrices, expanding the theory of special matrix functions.

Contribution

It presents novel definitions and properties of generalized incomplete exponential matrix functions, including integral, differential, addition, multiplication, and recurrence formulas.

Findings

Derived new integral and differential formulas for matrix functions.

Established connections with incomplete gamma, Bessel, and modified Bessel matrix functions.

Contributed to the theoretical development of special matrix functions.

Abstract

The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence relation obtained here are believed to be new in the theory of special matrix functions. We also establish the connection between these matrix functions and other matrix functions, such as the incomplete gamma matrix function, the Bessel and modified Bessel matrix functions.