Integral proofs of two alternating sign binomial coefficient identities

Abstract

An alternating sign binomial coefficient identity - available computationally from both a mainstream and specialist algebraic software package, and also as a special case of an analytic result due to P. Kirschenhofer - is proven in a novel way via integration. The method generates another, more complex, identity of the same type in a similar way and can be extended in principle to develop further results.