Volume 34, Number 1 - December 1954

Volume 34, Number 1 - December 1954. 33 pages including covers and advertisements. Editorials Reverend Chu-Công, Joseph, Communists and Christmas in Viet-nam McLarney, James J., Mr. Spindly Tousignant, Louis, The Beauty of Simplicity McLarney, James J., Redress and Grievance McLarney, James J., Ques

Marissa Plati, mezzo-soprano and Hoi Ting Chu, piano, April 7, 2017

This is the concert program of the Marissa Plati, mezzo-soprano and Hoi Ting Chu, piano performance on Friday, April 7, 2017 at 8:00 p.m., at the Concert Hall, 855 Commonwealth Avenue. Works performed were Madre diletta, abbracciami by Giovanni Porta,Die Mainacht by Johannes Brahms, Immer leise wird mein Schlummer by J. Brahms, Von ewiger Liebe by J. Brahms, Il Tramonto by Ottorino Respighi, Banalités by Francis Poulenc, and This is Just to Say by Francis Snyder. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

Some vanishing sums involving binomial coefficients in the denominator

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 Chu-Vandermonde 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 well-known [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

Evaluations of some terminating hypergeometric ₂F₁(2) series with applications

Explicit expressions for the hypergeometric series 2F1(-n, a; 2a±j; 2) and 2F1(-n, a;-2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j| ≤ 5 derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating 3F2(2) series and the confluent hypergeometric function 1F1(x).</p