Modelling the interaction of nanotube with particles of the medium by the Green's function method

The end surface of a cylindrical nanotube is considered as an annular and is replaced by a torus by solving the electrostatic problems, they are 1) the interaction of a charged particle with a torus and 2) the interaction of a charged torus with a neutral particle. Solution of the Poisson equation is given in the toroidal coordinate system and expressed by a half-order Legendre function of the first and second kind. The convergence of series expansion is improved by a given transformation of corresponding hypergeometric functions. The calculations are represented for the axially symmetric case.