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Some properties of proximate orders for analytic functions. (English) Zbl 0673.30019

Proximate orders \(\rho\) (r) for entire functions were constructed by G. Valiron [Lectures on the general theory of integral functions, pp. 64-67] for comparing the growth of log M(r,f) with that of \(r^{\rho (r)}\). Later on the reviewer gave another method [S. M. Shah, Bull. Am. Math. Soc. 52, 326-328 (1946; Zbl 0061.151)] for this construction [see also M. L. Cartwright, Integral functions (1956; Zbl 0075.059)]. O. P. Juneja and G. P. Kapoor worked out a proximate order \(\rho\) (r) for a function analytic in the unit disc D. The author constructs a proximate order for a function analytic in D having finite positive order under certain conditions.
Reviewer: S.M.Shah

MSC:

30D15 Special classes of entire functions of one complex variable and growth estimates
30C50 Coefficient problems for univalent and multivalent functions of one complex variable

Keywords:

proximate order
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