Finite-order meromorphic solutions and the discrete Painleve equations

R. G. Halburd, R. J. Korhonen

Let w(z) be a finite-order meromorphic solution of the second-order difference equation w(z+1)+w(z-1) = R(z,w(z)) (eqn 1) where R(z,w(z)) is rational in w(z) and meromorphic in z.…