Name: Stirling’s Approximation for Central Extended Binomial Coefficients
Creator: Steffen Eger
Keywords: FOS: Computer and information sciences, Discrete Mathematics (cs.DM), 13. Climate action, Probability (math.PR), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 0102 computer and information sciences, 0101 mathematics, 7. Clean energy

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2014Embargo end date: 01 Jan 2012Publisher:Informa UK LimitedJournal:The American Mathematical Monthly, volume 121, page 344 (issn: 0002-9890,

Authors: Steffen Eger;

doi: 10.4169/amer.math.monthly.121.04.344 , 10.48550/arxiv.1203.2122

arXiv: http://arxiv.org/abs/1203.2122

Stirling’s Approximation for Central Extended Binomial Coefficients

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Abstract

We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients. To do so, we relate the exact distribution of the sum of independent discrete uniform random variables to the asymptotic distribution, obtained from the Central Limit Theorem and a local limit variant.

Slight modification of journal version; title fixed

Keywords

FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Probability (math.PR), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics - Probability, Computer Science - Discrete Mathematics

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