Some relations on ultraspherical matrix polynomials ∗

Ayman Shehata; Lalit Mohan Upadhyaya; Shimaa I Moustafa

doi:10.48165/

Authors

Ayman Shehata Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt.
Lalit Mohan Upadhyaya Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, India-248179
Shimaa I Moustafa Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt

DOI:

https://doi.org/10.48165/

Keywords:

Functional matrix calculus, Hermite, Laguerre, Ultraspherical, matrix polynomials

Abstract

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 be tween 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.

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