A note on generating functions for the unification of the Bernstein type basis functions

Abstract

In [3], Simsek unified generating function of the Bernstein basis functions. In this paper, by using knot sequence, we rewrite generating functions for the unification of the Bernstein type basis functions. By using these generating functions, we also find generating function for the Hermite type numbers. We investigate some properties of this functions and these basis. Finally, we simulate these polynomials with their plots for some selected numerical values.