Expressions for Neutrino Wave Functions and Transition Probabilities at   Three Neutrino Oscillations in Vacuum and Some of Their Applications
  We have considered three neutrino transitions and oscillations in the general case and obtained expressions for neutrino wave functions in three cases: with CP violation, without CP violations and the case when $\nu_e \leftrightarrow \nu_\tau$ transitions are absent (some works indicate on this possibility). Then using the existing experimental data some analysis has been fulfilled. This analysis definitely has shown that transitions $\nu_e \leftrightarrow \nu_\tau$ cannot be closed for the Solar neutrinos. However, this possibility may be realized by using the mechanism of resonance enhancement neutrino oscillations in matter (the Sun). But this possibility is not confirmed by the Solar neutrinos spectrum (the Solar neutrinos spectrum is not distorted) and the Day-Night effect (this effect is not observed). It was found out that the probability of $\nu_e \leftrightarrow \nu_e$ neutrino transitions is positive defined value only if the angle of $\nu_e, \nu_\tau$ mixing $\beta \le 15^o \div 17^o$. 
Kh. M. Beshtoev