The Journal of the Indian Mathematical Society

J. Gopala Krishna ¹

Affiliations
1 Andhra University, Waltair, IN

Abstract

Let P(z) = Σ a_kz^k be an entire series. Let M (r), n{r), v(r), and μ(r) stand, as usual [1] for the 'Maximum modulus' etc. of P and let I(r) be the 'logarithmic mean of P' viz. (l/2π) ∫ log|P(r e^tθ)| dθ.

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J. Gopala Krishna ¹

Affiliations
1 Department of Mathematics, Andhra University, Waltair, IN

Abstract

Let P (z) be a non-constant entire function throughout and let, as usual (Ch. II of [1]), the functions M(r:P) and n (r:P) be the maximum modulus and the counting function of the zeros of P and let μ (r : P) and v (r : P) be the maximum term and its rank, associated with the Maclaurin Expansion of P.

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