Some Double Sums Involving Ratios ofBinomial Coefficients ArisingFrom Urn Models

A1 Journal article (refereed)


Internal Authors/Editors


Publication Details

List of Authors: David Stenlund, James Gu Feng Wan
Publisher: University of Waterloo
Publication year: 2019
Journal: Journal of Integer Sequences
Volume number: 22


Abstract

In this paper we discuss a class of double sums involving ratios of binomial coefficients. The sums are of the form

egin{displaymath}sum_{j=0}^{n} sum_{i=0}^j rac{inom{f_1(n)}{i}}{inom{f_2(n)}{j}},c^{i-j}, end{displaymath}

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.


Keywords

Binomial identities, Hypergeometric functions, Urn models

Last updated on 2020-25-02 at 04:48