## Modified Mathieu functions for radial Schroedinger equation with polarization potential: Reliable numerical algorithms

The new numerical approach to calculation of modified Mathieu functions is proposed. These functions play an important role in theories of electron scattering from (highly) polarizable atoms, like alkalis. The algorithms we developed show very high accuracy in a wide range of energy and polarizability, which are the two principal parameters of the problem. The numerical scheme does not lose the accuracy in the so called {open_quotes}unstable{close_quotes} regions, where the characteristic exponent of Mathieu functions becomes complex. This stability makes possible the analytical continuation of these methods in the complex plane of parameters.