\[{{}_{p}F_{q}}\left({a_{1}+r,\dots,a_{p}+r\atop b_{1}+r,\dots,b_{q}+r};z\right)%
=\sum_{n=0}^{m-1}\frac{{\left(a_{1}+r\right)_{n}}\cdots{\left(a_{p}+r\right)_{%
n}}}{{\left(b_{1}+r\right)_{n}}\cdots{\left(b_{q}+r\right)_{n}}}\frac{z^{n}}{n%
!}+O\left(\frac{1}{r^{(q-p)m}}\right),\]