\[{{}_{4}F_{3}}\left({-n,a,b,c\atop d,e,f};1\right)=\frac{{\left(e-a\right)_{n}}%
{\left(f-a\right)_{n}}}{{\left(e\right)_{n}}{\left(f\right)_{n}}}{{}_{4}F_{3}}%
\left({-n,a,d-b,d-c\atop d,a-e-n+1,a-f-n+1};1\right),\]