# §16.6 Transformations of Variable

 16.6.1 $\mathop{{{}_{3}F_{2}}\/}\nolimits\!\left({a,b,c\atop a-b+1,a-c+1};z\right)=(1-% z)^{-a}\mathop{{{}_{3}F_{2}}\/}\nolimits\!\left({a-b-c+1,\frac{1}{2}a,\frac{1}% {2}(a+1)\atop a-b+1,a-c+1};\frac{-4z}{(1-z)^{2}}\right).$
 16.6.2 $\mathop{{{}_{3}F_{2}}\/}\nolimits\!\left({a,2b-a-1,2-2b+a\atop b,a-b+\frac{3}{% 2}};\frac{z}{4}\right)=(1-z)^{-a}\mathop{{{}_{3}F_{2}}\/}\nolimits\!\left({% \frac{1}{3}a,\frac{1}{3}a+\frac{1}{3},\frac{1}{3}a+\frac{2}{3}\atop b,a-b+% \frac{3}{2}};\frac{-27z}{4(1-z)^{3}}\right).$
For Kummer-type transformations of $\mathop{{{}_{2}F_{2}}\/}\nolimits$ functions see Miller (2003) and Paris (2005a), and for further transformations see Erdélyi et al. (1953a, §4.5) and Miller and Paris (2011).