\[{{}_{3}F_{2}}\left({a_{1}+2,a_{2},a_{3}\atop b_{1},b_{2}};z\right)a_{1}(a_{1}+%
1)(1-z)+{{}_{3}F_{2}}\left({a_{1}+1,a_{2},a_{3}\atop b_{1},b_{2}};z\right)a_{1%
}\left(b_{1}+b_{2}-3a_{1}-2+z(2a_{1}-a_{2}-a_{3}+1)\right)+{{}_{3}F_{2}}\left(%
{a_{1},a_{2},a_{3}\atop b_{1},b_{2}};z\right)\left((2a_{1}-b_{1})(2a_{1}-b_{2}%
)+a_{1}-a_{1}^{2}-z(a_{1}-a_{2})(a_{1}-a_{3})\right)-{{}_{3}F_{2}}\left({a_{1}%
-1,a_{2},a_{3}\atop b_{1},b_{2}};z\right)(a_{1}-b_{1})(a_{1}-b_{2})=0.\]