  The explicit formulas for the maps interconnecting the sets of solutions of
the special double confluent Heun equation and the equation of the RSJ model of
overdamped Josephson junction in case of shifted sinusoidal bias are given. The
approach these are based upon leans on the extensive application of
eigenfunctions of certain linear operator acting on functions holomorphic on
the universal cover of the punctured complex plane. The functional equation the
eigenfunctions noted obey is derived, the matrix form of the monodromy
transformation they infer is given.
