  Finite hypergeometric functions are functions of a finite field ${\bf F}_q$
to ${\bf C}$. They arise as Fourier expansions of certain twisted exponential
sums and were introduced independently by John Greene and Nick Katz in the
1980's. They have many properties in common with their analytic counterparts,
the hypergeometric functions. One restriction in the definition of finite
hypergeometric functions is that the hypergeometric parameters must be rational
numbers whose denominators divide $q-1$. In this note we use the symmetry in
the hypergeometric parameters and an extension of the exponential sums to
circumvent this problem as much as posssible.
