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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.
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Jacek Cichoń, Zbigniew Gołębiewski. On Bernoulli Sums and Bernstein Polynomials. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. pp.179-190. ⟨hal-01197242⟩

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