Stirling’s Approximation for Central Extended Binomial Coefficients

Stirling’s Approximation for Central Extended Binomial Coefficients

We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients, using the distribution of the sum of independent discrete uniform random variables with the Central Limit Theorem and a local limit variant.

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Bibliographische Detailangaben
Veröffentlicht in:The American mathematical monthly 2014-04, Vol.121 (4), p.344-349
1. Verfasser: Eger, Steffen
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Asymptotic methods
Binomial coefficients
Binomials
Coefficients
Polynomials
Random variables
Theorems
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Beschreibung
Zusammenfassung:We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients, using the distribution of the sum of independent discrete uniform random variables with the Central Limit Theorem and a local limit variant.
ISSN:0002-9890
1930-0972
DOI:10.4169/amer.math.monthly.121.04.344