On numerical evaluation of the Heun functions

In the paper we deal with the Heun functions - solutions of the Heun equation. Despite the increasing interest to the equation and numerous applications of the functions in a wide variety of physical problems, it is only Maple amidst known software packages which is able to evaluate the functions numerically. But the Maple routine is known to be imperfect. The purpose of the work is to develop alternative algorithms for numerical evaluation of the Heun functions. A procedure based on power series expansions and analytic continuation is suggested.