  Israel M. Gelfand gave a geometric interpretation for general hypergeometric
functions as sections of the tautological bundle over a complex Grassmannian
$G_{k,n}$. In particular, the beta function can be understood in terms of
$G_{2,3}$. In this manuscript, we construct one of the simplest generalizations
of the Euler beta function by adding arbitrary-many odd variables to the
classical setting. We also relate the beta super-function to the gamma and the
hypergeometric function.
