A Note on Extended Binomial Coefficients

2014/07/28 by Thorsten Neuschel, Neuschel, Thorsten · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #math.CA #math.CO

paper · pdf · doi:10.48550/arxiv.1407.7429

arxiv created 2014/07/28 · arxiv updated 2014/07/29

Abstract

We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as sums of Hermite polynomials and Bernoulli numbers.

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