Nonpower expansions of solutions to the third Painlev'e equation

Abstract:

We consider the third Painlev´e equation in the case when all its four complex parameters are non-zero. For this case, all families of power expansions of its solutions near zero and infinity have been found in the preprint no. 51 for 2003. Here we calculate exponential additions to power expansions of its solutions near infinity (§1), all families of power-logarithmic expansions of its solutions near zero (§ 2) and all families of complicated expansions of its solutions near zero (§ 3).

Publication language:russian,
pages:21

Research direction:

Mathematical problems and theory of numerical methods