TY - JOUR
AU - Toppila, Sakari
AB - ON THE DEFICIENCIES OF A MEROMORPHIC FUNCTION AND OF ITS DERIVATIVE SAKARI TOPPILA 1. Introduction and results We shall employ the usual notation of Nevanlinna theory. Let / be meromorphic in the plane. The Nevanlinna deficiency is defined by 8{aJ) = hminf T(rj) and the Valiron deficiency by Let / have finite order and be transcendental. Then we have the classical inequality m(r,f) ^ m(r,f) + o(T(r,f)) as r -+ oo (1) which implies, together with the fact that N(r,f)^N(r,f')^2N(r,f), (2) that S(oo,f) ^ S(co,f) (3) and Let a be a finite complex value. Then m(r, a, f) = ml r, • 77 K m(r, /'/(/-a)) + m(r, 0, /' ) V J~ J J and we deduce that m(r,a,f) ^ m(r,0, f') + o(T(r, f)) as r -> 00 . (5) From (1) and (2) we deduce that T(r,f) ^ (2 + o(l))T(r,/ ) as r -> 00 , (6) and we conclude from (5) that S(a,f)^25(0,f) (7) Received 19 December, 1980; revised 14 May, 1981. [J. LONDON MATH. SOC. (2), 25 (1982), 273-287] 27 4 SAKARI TOPPILA and ') (8) for transcendental meromorphic functions of a finite order. In the other direction, we prove the following. THEOREM 
TI - On the Deficiencies of a Meromorphic Function and of its Derivative
JF - Journal of the London Mathematical Society
DO - 10.1112/jlms/s2-25.2.273
DA - 1982-04-01
UR - https://www.deepdyve.com/lp/wiley/on-the-deficiencies-of-a-meromorphic-function-and-of-its-derivative-KOwMS5Kc0h
SP - 273
EP - 287
VL - s2-25
IS - 2
DP - DeepDyve
ER -