Some Double Sums Involving Ratios of Binomial Coefficients Arising From Urn Models

2018/09/25 by David Stenlund, Stenlund, David, J. G. Wan +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1809.09634

openalex publication_date 2018/09/25 · openalex created_date 2018/10/05 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss a class of double sums involving ratios of binomial coefficients. The sums are of the form ∑_j=0ⁿ ∑_i=0^j \frac\binomf₁(n)i\binomf₂(n)j c^i-j, where f₁, f₂ are functions of n. Such sums appear in the analyses of the Mabinogion urn and the Ehrenfest urn in probability. Using hypergeometric functions, we are able to simplify these sums, and in some cases express them in terms of the harmonic numbers.

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• Double sums associated with binomial transforms
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