Extended analogues of gamma and beta matrix functions
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This paper explores the four-parameter Mittag-Leffler matrix function and discusses some of its properties, including Jordan decomposition. Some graphs are plotted for scalar functions. The new extended gamma matrix function(EGMF) and extended beta matrix function(EBMF) are proposed in conjunction with the four-parameter Mittag-Leffler matrix function. Various properties of these functions, including symmetry relationships, integral representations, generating relations, summation formulas and functional relations, have been investigated.
Abstract
This paper explores the four-parameter Mittag-Leffler matrix function and discusses some of its properties, including Jordan decomposition. Some graphs are plotted for scalar functions. The new extended gamma matrix function(EGMF) and extended beta matrix function(EBMF) are proposed in conjunction with the four-parameter Mittag-Leffler matrix function. Various properties of these functions, including symmetry relationships, integral representations, generating relations, summation formulas and functional relations, have been investigated.