In this paper we prove the following theorem:
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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
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$K(f^{(k)}) = \frac{2k(1 - \delta(\infty, f))} {1 + k - k\delta
(\infty, f)},$
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where
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$ K(f^{(k)}) = \lim \limits_{r \rightarrow \infty } (N(r, 1 /
f^{(k)}) + N(r,f^{(k)})) / T(r,f^{(k)})$ exists.
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This result improves the results by S. K. Singh and V. N. Kulkarni
[1] and Mingliang Fang [2].