\[F\left({-m,b\atop c};z\right)=\frac{{\left(c-b\right)_{m}}}{{\left(c\right)_{m%
}}}F\left({-m,b\atop b-c-m+1};1-z\right)=\frac{{\left(c-b\right)_{m}}}{{\left(%
c\right)_{m}}}z^{m}F\left({-m,1-c-m\atop b-c-m+1};1-\frac{1}{z}\right),\]