\[F\left({a,b\atop c};z\right)F\left({a,b\atop c};\zeta\right)=\sum_{s=0}^{%
\infty}\frac{{\left(a\right)_{s}}{\left(b\right)_{s}}{\left(c-a\right)_{s}}{%
\left(c-b\right)_{s}}}{{\left(c\right)_{s}}{\left(c\right)_{2s}}s!}\left(z%
\zeta\right)^{s}F\left({a+s,b+s\atop c+2s};z+\zeta-z\zeta\right),\]