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An analytical method for scalar second‐order functional‐difference equations with meromorphic periodic coefficients is proposed. The technique involves reformulating the equation as a vector functional‐difference equation of the first order and reducing it to a scalar Riemann–Hilbert problem for two finite segments on a hyperelliptic surface. The final step of the procedure is solution of the clas...

Second-order functional-difference equations. I: Method of the Riemann-Hilbert problem on Riemann surfaces