Kodai Mathematical Journal

Meromorphic function of infinite order with maximum deficiency sum

Weiling Xiong

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Abstract

In this paper we prove the following theorem: % Let $f(z)$ be a meromorphic function of infinite order. If $ \sum \limits_{a \neq \infty} \delta (a,f) + \delta (\infty, f) = 2,$ then for each positive integer $k$, we have % $K(f^{(k)}) = \frac{2k(1 - \delta(\infty, f))} {1 + k - k\delta (\infty, f)},$ % where % $ K(f^{(k)}) = \lim \limits_{r \rightarrow \infty } (N(r, 1 / f^{(k)}) + N(r,f^{(k)})) / T(r,f^{(k)})$ exists. % This result improves the results by S. K. Singh and V. N. Kulkarni [1] and Mingliang Fang [2].

Article information

Source
Kodai Math. J., Volume 27, Number 2 (2004), 105-113.

Dates
First available in Project Euclid: 24 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1093351318

Digital Object Identifier
doi:10.2996/kmj/1093351318

Mathematical Reviews number (MathSciNet)
MR2069762

Zentralblatt MATH identifier
1063.30032

Citation

Xiong, Weiling. Meromorphic function of infinite order with maximum deficiency sum. Kodai Math. J. 27 (2004), no. 2, 105--113. doi:10.2996/kmj/1093351318. https://projecteuclid.org/euclid.kmj/1093351318


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