= Solution
The <Papperitz symbol>
$$
P\left\{
\begin{matrix}
a&b&c\\
\alpha&\beta&\gamma\\
\alpha'&\beta'&\gamma'
\end{matrix};z
\right\}
$$
represents the two-dimensional <solution space of a homogeneous linear differential equation> for a second-order <Fuchsian differential equation> on the <Riemann sphere>. Its only singularities are the three <regular singular points> $a,b,c$. The two entries beneath each point are its <characteristic exponents at a regular singular point>: for example, in the nonresonant case a local basis near $a$ has leading behaviours $(z-a)^\alpha$ and $(z-a)^{\alpha'}$. If one of the points is infinity, exponent $\rho$ conventionally means behaviour $z^{-\rho}$ there.
The six exponents obey the <Fuchs relation>
$$
\boxed{\alpha+\alpha'+\beta+\beta'+\gamma+\gamma'=1}.
$$
Subject to this relation, the symbol determines the corresponding Riemann differential equation; resonant differences between exponents may produce <Logarithmic Frobenius solutions> without changing the exponent data recorded by the symbol.
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