MMN-1126
Some relations on Konhauser matrix polynomials
Abstract
This paper deals with the study of the generalized hypergeometric matrix function and obtain
some of its properties. We rephrase some results from the previous works that will be used in
this study. Our main aim in this paper is to investigate an extension of the Konhauser matrix
polynomials ZA
n (x; k) and deals with the expansion of matrix functions in series of Konhauser
matrix polynomials. We obtain the hypergeometric matrix function representation, matrix
differential equation, generating matrix functions, bilinear generating matrix functions, matrix
recurrence relations, finite summation formulas and related results for the Konhauser matrix
polynomials. An explicit expression for Konhauser matrix polynomials are given. Some relevant
matrix functions appear in terms of the Konhauser matrix polynomials. Finally, we obtain some
important results involving properties of Mittag-Leffler and Bessel-Maitland matrix functions
as applications.
Vol. 17 (2016), No. 1, pp. 605-633
DOI: 10.18514/MMN.2016.1126