Some Representations of the Modified Degenerate Gamma Matrix Function

The main goal of this article is to extend the concept of special matrix functions through the study of modified degenerate Gamma matrix function. For this, the modified degenerate Gamma matrix function has been introduced and some of its properties have been established. The article also presents limit representations, asymptotic equality, and infinite product representations. The new function of matrix argument is an analogue of the Gamma matrix function, and the properties are analogues of those satisfied by the Gamma matrix function. Upon taking the limit as \lambda \to ۰^{+}, the established results reduce to the results of the Gamma matrix function.

Keywords:

Modified degenerate Gamma function , Matrix functional calculus , Matrix factorial function , Gamma matrix function , Degenerate Gamma matrix function