I'm reading this article, where the main result which relates the tree Hypergeometric functions ${_2F_1}(a_1+\alpha_i,a_2+\beta_i;a_3+\gamma_i;z)$, $i=1,2,3$ is given in theorem 3, page 297. In tables 1-3 they give some samples of the values for $G_i$, $H_i$ and $C_i$ for various shifts $\alpha_i,\beta_i,\gamma_i$.
However I fail to reproduce such results. For example the case when $\alpha_2=1,\alpha_3=-1$, I get (c.f.equation after 2.6) $$\begin{pmatrix}G_2\\H_2\end{pmatrix}=\begin{pmatrix}0 & 0\\1 & 1\end{pmatrix}\begin{pmatrix}0 & 0\\1 & 1\end{pmatrix}\begin{pmatrix}1\\0\end{pmatrix}=\begin{pmatrix}0\\1\end{pmatrix}$$, while according to table 1 the result should be $$\begin{pmatrix}G_2\\H_2\end{pmatrix}=\begin{pmatrix}\frac{a_1(z-1)}{a_1-a_3}\\-\frac{a_3+a_1(z-2)-a_2 z}{a_1-a_3}\end{pmatrix}$$
What am I doing wrong here ?
