The final set of meromorphic and entire functions

The final set of a meromorphic function is introduced and a theorem of Polya is proved in detail to determine such sets for any meromorphic function. A close study of the zeros of some classical polynomials is given in order to determine the zeros of the successive derivatives of some meromorphic and entire functions. Also a quick analysis of the zeros of the successive derivatives of an entire function using some restrictions on the function and its zeros is done, followed by a brief look on the most recent developments on the zero sets of entire functions.