A Chaundy–Bullard type identity involving the Pochhammer symbol

Abstract

In this short note we use the combinatorial identity of Chaundy and Bullard to prove several identities involving the Pochhammer symbol. For example, it is proven that (Y)n+1∑k=0mn+kk(X)k(X+Y)n+k+1+(X)m+1∑k=0nm+kk(Y)k(X+Y)m+k+1=1where the Pochhammer symbol, or the rising factorial, is denoted by (z)n.