A new proof of an identity of Jetter and Stöckler for multivariate Bernstein polynomials

A simple proof of an elegant identity for multivariate Bernstein polynomials discovered recently by K. Jetter and J. Stöckler is given. This identity shows a pointwise orthogonality relation of multivariate Bernstein polynomials and implies a new representation for the dual basis of multivariate Bernstein polynomials. Our method is based on “generating functions”, which reveals a general structure of the identity.