  Using gradient expansion method the particle density, the energy and the
action were calculated at the formation of a vortex-skyrmion at high magnetic
field. No approximation of single Landau level was used contrary to other
papers on the subject. Taking into account the nearest Landau levels
essentially changes the expression for the vortex energy and gives some simple
physical interpretation of the main results. The local electron density
coincides with the local density of states. It is shown that the formation of a
vortex skyrmion gives the gain in the thermodynamic energy in the limit of
alarge magnetic field and a small value of the g-factor. That means a
spontaneous formation of vortices in this case. The Hopf term in the
vortex-skyrmion action is calculated and corresponds to the fermionic picture.
