COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. The routine COULCC calculates both the oscillating and the exponentially varying Coulomb wave functions, and their radial derivatives, for complex η (Sommerfeld parameter), complex energies and complex angular momenta. The functions for uncharged scattering (spherical Bessels) and cylindrical Bessel functions are special cases which are more easily solved. Two linearly independent solutions are found, in general, to the differential equation f ” (x)+g(x)f(x)=0, where g(x) has x 0 , x -1 and x -2 terms, with coefficients 1, -2η and -λ(λ+1), respectively.