Bivariate Bernstein polynomials that reproduce exponential functions

Generalized Bernstein Polynomials and Symmetric Functions

We begin by classifying all solutions of two natural recurrences that Bernstein polynomials satisfy. The first scheme gives a natural characterization of Stancu polynomials. In Section 2, we identify the Bernstein polynomials as coefficients in the generating function for the elementary symmetric functions, which gives a new proof of total positivity for Bernstein polynomials, by identifying th...

Weighted Markov–bernstein Inequalities for Entire Functions of Exponential Type

We prove weighted Markov–Bernstein inequalities of the form

Some Results on Bernstein-sato Polynomials for Parametric Analytic Functions

This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in the case of one function. We also make an extensive study of an example for which we give an expression of a generic (and under some conditions, a relative) B...

Approximation properties of bivariate complex q - Bernstein polynomials in the case

Bivariate generalized exponential distribution

Recently it is observed that the generalized exponential distribution can be used quite effectively to analyze lifetime data in one dimension. The main aim of this paper is to define a bivariate generalized exponential distribution so that the marginals have generalized exponential distributions. It is observed that the joint probability density function, the joint cumulative distribution funct...