Explain what is meant by the Papperitz symbol

$$P\left\{\begin{array}{cccc} z_{1} & z_{2} & z_{3} & \\ \alpha & \beta & \gamma & z \\ \alpha^{\prime} & \beta^{\prime} & \gamma^{\prime} & \end{array}\right\}$$

The hypergeometric function $F(a, b ; c ; z)$ is defined as the solution of the equation determined by the Papperitz symbol

$$P\left\{\begin{array}{ccc} 0 & \infty & 1 \\ 0 & a & 0 \\ 1-c & b & c-a-b \end{array}\right\}$$

that is analytic at $z=0$ and satisfies $F(a, b ; c ; 0)=1$.

Show, explaining each step, that

$$F(a, b ; c ; z)=(1-z)^{c-a-b} F(c-a, c-b ; c ; z)$$