On the coefficients of a function analytic in the unit disc having slow rate of growth
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For a function f, analytic in z < 1, the notions of generalized orders are introduced that are specially suited for the study of the growth of f, if it is of slow growth. The characterizations of the generalized orders are found in terms of the coefficients in the Taylor series development of f. A decomposition theorem is proved for functions of hirregular growth. The results of the present paper generalize the results in [G. P. Kapoor - K. Gopal, J. Math. Anal. Appl., 74 (1980), pp. 446–455].
KeywordsSlow Growth Slow Rate Taylor Series Unit Disc Generalize Order
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