\[\lim_{|\alpha|\to\infty}{{}_{p+1}F_{q}}\left({a_{1},\dots,a_{p},\alpha\atop b_%
{1},\dots,b_{q}};\frac{z}{\alpha}\right)={{}_{p}F_{q}}\left({a_{1},\dots,a_{p}%
\atop b_{1},\dots,b_{q}};z\right).\]