Generating functions for polynomials derived from central moments involving bernstein basis functions and their applications

Abstract

AbstractThe main objective of this article is to construct generating functions for central moments involving Bernstein basis functions. We give some alternating generating functions of these functions. We also give derivative formulas and a recurrence relation of central moments with the help of their generating functions. We also establish new relations between combinatorial numbers and polynomials, and also central moments. Furthermore, by applying Euler operator and Laplace transformation to central moments, we derive some important results. Finally, we give further remarks, observations and comments related to the content of this paper.