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A basis of the solution space of a homogeneous linear differential equation for the Mészáros equation on $y>0$ isSubstitution verifies both solutions; their Wronskian is $-1/[y\sqrt{1+y}]$, so they are independent. At small $y$, $D_{+}=1+O(y)$ and $D_{-}=\log (4/y)-3+O(y\log y)$. At large $y$, $D_{+}\sim 3y/2$ and $D_{-}\sim 4/(15y^{3/2})$. Matching the actual early-time radiation forcing determines which constant and logarithmic combination is excited.

The Papperitz symbolrepresents 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 $(z-a{)}^{{\alpha }^{\prime }}$. If one of the points is infinity, exponent $\rho$ conventionally means behaviour $z^{-\rho }$ there.

The six exponents obey the Fuchs relationSubject 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.