Kasana, H. S. Proximate order and lower type of entire gap power series. (English) Zbl 1042.30014 Jap. J. Math., New Ser. 29, No. 1, 15-25 (2003). 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. Reviewer: Polina Z. Agranovich (Khar’kov) MSC: 30D15 Special classes of entire functions of one complex variable and growth estimates 30B10 Power series (including lacunary series) in one complex variable Keywords:entire function; proximate order; index-pair; type PDFBibTeX XMLCite \textit{H. S. Kasana}, Jpn. J. Math., New Ser. 29, No. 1, 15--25 (2003; Zbl 1042.30014)