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Generalized Mittag-Leffler Matrix Function and Associated Matrix Polynomials


Affiliations
1 Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, India
2 Ramrao Adik Institute of Technology, Navi Mumbai, India
3 Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara, India
     

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The Mittag-Leffler function has been found useful in solving certain problems in Science and Engineering. On the other hand, noticing the occurrence of certain matrix functions in Special functions’ theory in general and in Statistics and Lie group theory in particular, we introduce here a matrix analogue of a recently generalized form of Mittag-Leffler function. This function yields the matrix analogues of the Saxena-Nishimoto’s function, Bessel-Maitland function, Dotsenko function and the Elliptic Function. We obtain matrix differential equation and eigen matrix function property for the proposed matrix function. Also, a generalized Konhauser matrix polynomial is deduced and its inverse series relations and generating function are derived.

Keywords

Mittag-Leffler Matrix Function, Matrix Differential Equation, Generalized Konhauser Matrix Polynomial, Generating Function.
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  • Generalized Mittag-Leffler Matrix Function and Associated Matrix Polynomials

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Authors

Reshma Sanjhira
Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, India
B. V. Nathwani
Ramrao Adik Institute of Technology, Navi Mumbai, India
B. I. Dave
Department of Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara, India

Abstract


The Mittag-Leffler function has been found useful in solving certain problems in Science and Engineering. On the other hand, noticing the occurrence of certain matrix functions in Special functions’ theory in general and in Statistics and Lie group theory in particular, we introduce here a matrix analogue of a recently generalized form of Mittag-Leffler function. This function yields the matrix analogues of the Saxena-Nishimoto’s function, Bessel-Maitland function, Dotsenko function and the Elliptic Function. We obtain matrix differential equation and eigen matrix function property for the proposed matrix function. Also, a generalized Konhauser matrix polynomial is deduced and its inverse series relations and generating function are derived.

Keywords


Mittag-Leffler Matrix Function, Matrix Differential Equation, Generalized Konhauser Matrix Polynomial, Generating Function.

References