Exploring probabilistic Bernstein polynomials: identities and applications

Abstract

In this paper, we introduce the probabilistic Bernstein polynomials and derive new and interesting correlations among several special functions and special number sequences such as Euler polynomials, Bernoulli polynomials of higher order, Frobenius–Euler polynomials of higher order, Stirling numbers of the second kind and Bell polynomials subject to several special random variables.

Keywords

• Probabilistic Bernstein polynomials
• probabilistic Bernoulli polynomials
• probabilistic Euler polynomials
• probabilistic Stirling numbers of the second kind
• random variable
• distributions