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Proximate order and lower type of entire gap power series. (English) Zbl 1042.30014

Let \(f (z) = \sum_{n=0}^{\infty} a_n z^{\lambda_n}\) be a nonconstant entire function, \(\lambda_0 = 0\), \(\{\lambda_n\}_{n=1}^{\infty} \not=\) is a strictly increasing sequence of positive integers. The author has obtained the representation of lower \((p,q)\)-type of this function with respect to a proximate order in terms of coefficients \(a_n\) and exponents \(\lambda_n\) (Theorems 1 and 2). These results have given the answer on the question formulated in the paper of Bajpai, Kapoor, Juneja.

MSC:

30D15 Special classes of entire functions of one complex variable and growth estimates
30B10 Power series (including lacunary series) in one complex variable
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