On Bernoulli Sums and Bernstein Polynomials

Abstract

In the paper we discuss a technology based on Bernstein polynomials of asymptotic analysis of a class of binomial sums that arise in information theory. Our method gives a quick derivation of required sums and can be generalized to multinomial distributions. As an example we derive a formula for the entropy of multinomial distributions. Our method simplifies previous work of Jacquet, Szpankowski and Flajolet from 1999.