1Department of Mathematics, College of Science and Arts, Unaizah, Qassim University, Qassim, Kingdom of Saudi Arabia.
2Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, India-248179.
3Department of Mathematics, Faculty of Science, Assiut University, Assiut71516, Egypt.
*E-mail: drshehata2006@yahoo.com
**E-mail: lmupadhyaya@rediffmail.com, hetchres@gmail.com
***E-mail: shimaa1362011@yahoo.com
The main aim of this work is to give a different approach to the proof of some properties for Ultraspherical matrix polynomials (UMPs). We obtain the connections between Laguerre, Hermite and Ultraspherical matrix polynomials. Some definitions of new families of Ultraspherical matrix polynomials are given. Finally, various families of linear, bilinear and bilateral generating matrix functions (GMFs) for UMPs are given.
Functional matrix calculus, Hermite, Laguerre, Ultraspherical, matrix polynomials, 15A60, 33C50, 42C05, 33D45
