Some Double Sums Involving Ratios ofBinomial Coefficients ArisingFrom Urn Models

David Stenlund; James Gu Feng Wan

Some Double Sums Involving Ratios ofBinomial Coefficients ArisingFrom Urn Models

David Stenlund
, James Gu Feng Wan

Tutkimustuotos: Lehtiartikkeli › Artikkeli › Tieteellinen › vertaisarvioitu

Abstrakti

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

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.

Alkuperäiskieli	Englanti
Sivut	–
Julkaisu	Journal of Integer Sequences
Vuosikerta	22
Tila	Julkaistu - 2019
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Keywords

Urn models
Binomial identities
Hypergeometric functions

Pääsy asiakirjaan

https://cs.uwaterloo.ca/journals/JIS/VOL22/Wan/wan2.html

Viittausmuodot

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title = "Some Double Sums Involving Ratios ofBinomial Coefficients ArisingFrom Urn Models",

abstract = "In this paper we discuss a class of double sums involving ratios of binomial coefficients. The sums are of the form 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 = "Urn models, Binomial identities, Hypergeometric functions, Urn models, Binomial identities, Hypergeometric functions, Urn models, Binomial identities, Hypergeometric functions",

author = "David Stenlund and \{Gu Feng Wan\}, James",

year = "2019",

language = "English",

volume = "22",

pages = "–",

journal = "Journal of Integer Sequences",

issn = "1530-7638",

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TY - JOUR

T1 - Some Double Sums Involving Ratios ofBinomial Coefficients ArisingFrom Urn Models

AU - Stenlund, David

AU - Gu Feng Wan, James

PY - 2019

Y1 - 2019

N2 - In this paper we discuss a class of double sums involving ratios of binomial coefficients. The sums are of the form 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.

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

KW - Urn models

KW - Binomial identities

KW - Hypergeometric functions

KW - Urn models

KW - Binomial identities

KW - Hypergeometric functions

KW - Urn models

KW - Binomial identities

KW - Hypergeometric functions

M3 - Article

SN - 1530-7638

VL - 22

SP - –

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

ER -

Some Double Sums Involving Ratios ofBinomial Coefficients ArisingFrom Urn Models

Abstrakti

Keywords

Pääsy asiakirjaan

Sormenjälki

Viittausmuodot