On a combinatorial identity of Chaundy and Bullard

Horst Alzer, Omran Kouba

We give two new proofs of the Chaundy-Bullard formula $$(1-x{)}^{n+1}\sum _{k=0}^m(\genfrac{}{}{0ex}{}{n+k}{k})x^k+x^{m+1}\sum _{k=0}^n(\genfrac{}{}{0ex}{}{m+k}{k})(1-x{)}^k=1$$ and we prove the "twin formula…