\[{{}_{3}F_{2}}\left({a_{1},a_{2},a_{3}\atop b_{1},b_{2}};\mathbf{I}\right)=%
\frac{\Gamma_{m}\left(b_{1}\right)\Gamma_{m}\left(b_{2}\right)\Gamma\left(c%
\right)}{\Gamma_{m}\left(a_{1}\right)\Gamma_{m}\left(c+a_{2}\right)\Gamma\left%
(c+a_{3}\right)}\*{{}_{3}F_{2}}\left({b_{1}-a_{1},b_{2}-a_{2},c\atop c+a_{2},c%
+a_{3}};\mathbf{I}\right),\]