DIRECT TRANSCENDENTAL SINGULARITIES FOR INVERSE FUNCTIONS OF MEROMORPHIC FUNCTIONS AND OF THEIR DERIVATIVES

This paper proves the following result: Let f（z） be a meromorphic function of order ρ and pi be thenumber of the distinct finite non-zero direct transcendental singularities of the inverse function of the i-thderivative of f（z） (f（z）≡f（z）). Then we haveP≤2ρ, if ρ≥1: p≤1, if 0≤ρ<1,where p = sum from i=0 to +∞（Pi）.