  We obtain a reflection formula for the Gaussian hypergeometric function of
real symmetric matrix argument. We also show that this result extends to the
Gaussian hypergeometric function defined over the symmetric cones, and even to
generalizations of the Gaussian hypergeometric function defined in terms of
series of Jack polynomials. Finally, we obtain a quadratic transformation
formula for the Gaussian hypergeometric function of Hermitian $2 \times 2$
matrix argument.
