\begin{definition}[Definition:Riemann P-symbol]
The '''Riemann P-symbol''', written: 
:$\map f z = \operatorname P \set {\begin {matrix} a & b & c \\ \alpha & \beta & \gamma & z \\ \alpha' & \beta' & \gamma' \end {matrix} }$
denotes the solutions to the hypergeometric differential equation: 
{{begin-eqn}}
{{eqn | o = 
      | r = \frac {\d^2 f} {\d z^2}
}}
{{eqn | o = 
      | ro= +
      | r = \paren {\frac {1 - \alpha - \alpha'} {z - a} + \frac {1 - \beta - \beta'} {z - b} + \frac {1 - \gamma - \gamma'} {z - c} } \frac {\d f} {\d z}
}}
{{eqn | o = 
      | ro= +
      | r = \paren {\frac {\alpha \alpha' \paren {a - b} \paren {a - c} } {z - a} + \frac {\beta \beta' \paren {b - c} \paren {b - a} } {z - b} + \frac {\gamma \gamma' \paren {c - a} \paren {c - b} } {z - c} } \frac f {\paren {z - a} \paren {z - b} \paren {z - c} }
}}
{{eqn | r = 0
}}
{{end-eqn}}
where:
:$\alpha + \alpha' + \beta + \beta' + \gamma + \gamma' = 1$
\end{definition}