\[{{}_{5}F_{4}}\left({a,\frac{1}{2}a+1,b,c,d\atop\frac{1}{2}a,a-b+1,a-c+1,a-d+1}%
;1\right)=\frac{\Gamma\left(a-b+1\right)\Gamma\left(a-c+1\right)\Gamma\left(a-%
d+1\right)\Gamma\left(a-b-c-d+1\right)}{\Gamma\left(a+1\right)\Gamma\left(a-b-%
c+1\right)\Gamma\left(a-b-d+1\right)\Gamma\left(a-c-d+1\right)},\]