  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. 
The interrelation of the special double confluent Heun equation and the   equation of RSJ model of Josephson junction revisited