Geodesic
On Bernoulli Sums and Bernstein Polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) (2012).

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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. 
@article{DMTCS_2012_special_262_a14,
     author = {Cicho\'n, Jacek and Go{\l}\k{e}biewski, Zbigniew},
     title = {On {Bernoulli} {Sums} and {Bernstein} {Polynomials}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)},
     year = {2012},
     doi = {10.46298/dmtcs.2993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2993/}
}
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Cichoń, Jacek; Gołębiewski, Zbigniew. On Bernoulli Sums and Bernstein Polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) (2012). doi : 10.46298/dmtcs.2993. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2993/

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