Some Properties of Generalized Gegenbauer Matrix Polynomials

Some identities involving generalized Gegenbauer polynomials

A new Extension of Gegenbauer Matrix Polynomials and Their Properties

The aim of this paper is to define and study of the Gegenbauer matrix polynomials of two variables. An explicit representation, a three-term matrix recurrence relations, differential recurrence relations and hypergeometric matrix representation for the Gegenbauer matrix polynomials of two variables are given. The Gegenbauer matrix polynomials are solutions of the matrix differential equations a...

Generalized numerical ranges of matrix polynomials

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

Some new properties of Generalized Bernstein polynomials

Let Bm(f) be the Bernstein polynomial of degree m. The Generalized Bernstein polynomials