Mathematics

We present a systematic construction of a family of second-order linear ODEs of the form
y′′ + r(z)y = 0 whose solutions are Liouvillian and arise from a logarithmic derivative s(z) ∈
C(z, √R) of algebraic degree exactly 2 over C(z). The construction places two poles at z = 0
and z = 1 with equal residues 1/4, yielding the potential r(z) = …