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Symmetry 2019, 11(2), 151; https://doi.org/10.3390/sym11020151

Two Variables Shivley’s Matrix Polynomials

1
School of Mathematics and Statistics, Central South University, Changsha 410083, China
2
Department of Mathematics, Faculty of Science for Girls, King Khalid University, Abha 61471, Saudi Arabia
3
Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
*
Author to whom correspondence should be addressed.
Received: 5 January 2019 / Revised: 20 January 2019 / Accepted: 21 January 2019 / Published: 29 January 2019
(This article belongs to the Special Issue Polynomials: Special Polynomials and Number-Theoretical Applications)
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Abstract

The principal object of this paper is to introduce two variable Shivley’s matrix polynomials and derive their special properties. Generating matrix functions, matrix recurrence relations, summation formula and operational representations for these polynomials are deduced. Finally, Some special cases and consequences of our main results are also considered.
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Keywords: Shivley’s matrix polynomials; Generating matrix functions; Matrix recurrence relations; summation formula; Operational representations Shivley’s matrix polynomials; Generating matrix functions; Matrix recurrence relations; summation formula; Operational representations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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He, F.; Bakhet, A.; Hidan, M.; Abdalla, M. Two Variables Shivley’s Matrix Polynomials. Symmetry 2019, 11, 151.

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