论文信息 - On the growth of a meromorphic function and its derivatives

On the growth of a meromorphic function and its derivatives

The relative rates of growth of a function F meromorphic in the complex plane and its q derivative F (q) are studied via the Nevanlinna Characteristics T(r.F)and T(r.F (q)) and It is shown that lim inf T(r.F)/T(r.F (q)) ≤ 3ethat for all meromorphic functions. A lower bound on the size of the set {r>1 T(r.F) T(r.F (q))for K 1 is obtained. The upper bounds established for T(r.F)/T(r.F′)justify in a weakened form an old conjecture of Nevanlinna.

W. K. Hayman | J. Miles | W. Hayman | Joseph R. Miles

[1] W. K. Hayman,et al. On the characteristic of functions meromorphic in the unit disk and of their integrals , 1964 .

[2] Fritz Gackstatter,et al. Zur Theorie der gewohnlichen Differentialgleichungen im Komplexen , 1980 .

[3] W. Hayman. On the Characteristic of Functions Meromorphic in the Plane and of their Integrals , 1965 .

[4] S. Toppila. On Nevanlinna's characteristic function of entire functions and their derivatives , 1977 .