  The double hypergeometric Kamp\'e de F\'eriet series $F^{0:3}_{1:1}(1,1)$
depends upon 9 complex parameters. We present three cases with 2 relations
between those 9 parameters, and show that under these circumstances
$F^{0:3}_{1:1}(1,1)$ can be written as a ${}_4F_3(1)$ series. Some limiting
cases of these transformation formulas give rise to new summation results for
special $F^{0:3}_{1:1}(1,1)$'s. The actual transformation results arose out of
the study of 9-$j$ coefficients.
