Meromorphic functions with one deficient value

Abstract

Let f(z) be a meromorphic function and write Here N(r, a) and T(r, f) have their usual meanings (see [4], [5]) and 0 ≧ |a| ≧ ∞. If δ(a, f) > 0 then a is said to be an exceptional (or deficient) value in the sense of Nevanlinna (N.e.v.), and if Δ(a, f) > 0 then a is said to be an exceptional value in the sense of Varliron (V.e.v.). The Weierstrass p(z) function has no exceptional value N or V. Functions of zero order can have atmost one N.e.v. [4, p. 114], but may have more than one V.e.v. (see [6], [8]). In this note we consider functions satisfying some regularity conditions and having one and only one exceptional value V.