The authors consider the Maryland model associated to the Schrödinger equation \[ \psi_{k+1} - E\psi_k + \psi_{k-1} + \lambda\cot(\pi(\omega k+\theta))\psi_k = 0\;,\;k\in \mathbb Z, \] where \(\omega\in(0,1)\setminus\mathbb Q\), \(\theta\in[0,1)\) and \(E\in \mathbb R\) is the so-called spectral parameter. Let \(l>0\) and \(\eta\in(-\pi,\pi)\) defined such that \[ \lambda = -2\sinh l\sin\eta\;,\;E=2\cosh l\cos\eta\;, \]
\[ F(z,\eta,l) = \begin{pmatrix} 2\cosh l\cos\eta + 2\sinh l\sin\eta\cot\pi z & -1 \\ 1 & 0 \end{pmatrix} \] and, for the equation \[ \psi_{k+1} = F(k\omega + \theta,\eta,\l)\psi_k\;,\;k\in \mathbb Z, \] both vector and matrix solutions are considered. Let \(P_k(\omega,\theta,\eta,l)\) be the matrix solution of the second equation such that \(P_0(\omega,\theta,\eta,l)=I_2\) for any \(N\in\mathbb Z\). The authors obtain an explicit formula (“renormalization”) connecting \(P_N(\omega,\theta,\eta,l)\) for any \(N\in \mathbb Z\) to the minimal meromorphic solution of the “complex Maryland equation” \[ \psi(z+\omega) - E\psi(z) + \psi(z-\omega) + \lambda\cot(\pi z)\psi(z) = 0\;,\;z\in\mathbb C. \]