  We study the phase transition to the superconducting state taking into
account the fluctuations of the order parameter and of the vector magnetic
field and discuss the question of the order of transition occuring in this
model. We use the field-theoretical renormalization group approach and consider
in two-loop approximation the gauge model for a superconductor, generalized to
a n/2 component complex order parameter. Special attention is being payed to
the fact, that the corresponding series might be asymptotic ones and therefore
have zero radius of convergence. We review different ways of analytical
continuation of the series and applying Pade analysis and Pade-Borel
resummation technique conclude that in the model under consideration still
exists a possibility for the second-order phase transition with the critical
exponents differing from those of a superfluid liquid.
