*Article* **Two Variables Shivley's Matrix Polynomials**

### **Fuli He 1, Ahmed Bakhet 1, M. Hidan 2 and M. Abdalla 2,3,\***


Received: 5 January 2019; Accepted: 21 January 2019; Published: 29 January 2019

**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.

**Keywords:** Shivley's matrix polynomials; Generating matrix functions; Matrix recurrence relations; summation formula; Operational representations

**MSC 2010:** 33C05; 33C45; 33E20; 15A60
