The Papperitz-Riemann P-symbol$$ \tag 1 y(z) = P \left\{ \begin{matrix} z_1 & z_2 & z_3 & \; \\ \alpha_1 & \alpha_2 & \alpha_3 & z \\ \beta_1 & \beta_2 & \beta_3 & \; \end{matrix} \right\} $$ is used to express the solutions of second order homogeneous complex differential equations of the form $$ y'' + p(z) y' + q(z) y = 0, $$ with $p$ and $q$ meromorphic functions with a finite number of regular singular points.
How many different solutions does the Riemann's P-symbol describe?
How many (if any) of them describe the same identical function, only represented differently by Laurent expansions around different singular points?
