The Library
Some vanishing sums involving binomial coefficients in the denominator
Tools
Purkait, S. (Soma) and Sury, B.. (2008) Some vanishing sums involving binomial coefficients in the denominator. Albanian Journal of Mathematics , Vol.2 (No.1). pp. 2732. ISSN 19301235

Text
WRAP_Purkait_27271PB.pdf  Published Version Download (301Kb)  Preview 
Official URL: http://journals.aulonapress.com/index.php/ajm/arti...
Abstract
Identities involving binomial coeffcients usually arise in situations where counting is carried out in two different ways. For instance, some identities obtained by
William Horrace [1] using probability theory turn out to be special cases of the ChuVandermonde identities. Here, we obtain some generalizations of the identities observed by Horrace and give different types of proofs; these, in turn, give rise to some other new identities. In particular, we evaluate sums of the form Pm j=0 (1) j j d (mj) (n+jj )
and deduce that they vanish when d is even and m = n > d=2.
It is wellknown [2] that sums involving binomial coeffcients can usually be expressed in terms of the hypergeometric functions but it is more interesting if such a function can be evaluated explicitly at a given argument. Identities such as the ones we prove could perhaps be of some interest due to the explicit evaluation possible.
The papers [3], [4] are among many which deal with identities for sums where the binomial coeffcients occur in the denominator and we use similar methods here.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Binomial coefficients 
Journal or Publication Title:  Albanian Journal of Mathematics 
Publisher:  Aulonna Press 
ISSN:  19301235 
Official Date:  2008 
Volume:  Vol.2 
Number:  No.1 
Page Range:  pp. 2732 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Open Access 
References:  [1] W.C.Horrace  On the di�erence of maxima from independent uniform samples and a hy 
URI:  http://wrap.warwick.ac.uk/id/eprint/49191 
Request changes or add full text files to a record
Actions (login required)
View Item 