The Journal of the Indian Mathematical Society

T. V. Lakshminarasimhan ¹

Affiliations
1 Department of Mathematics, Madras Christian College, Tambaram, IN

Abstract

An entire function f(z) ≠ 0 is said to be of bounded index in the sense of Lepson ([6], pp. 304-305) if there exists an integer M.

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T. V. Lakshminarasimhan ¹

Affiliations
1 Madras Christian College, Tambaram (Madras), IN

Abstract

Then f(s) is bounded in any left half-plane, in particular, along any vertical line.

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T. V. Lakshminarasimhan ¹

Affiliations
1 Madras Christian College, Tambaram, IN

Abstract

Theorem 1 and Corollary 1 of this note are refinements of a Tauberian theorem of R. C. Buck [2, p. 148]. From these I deduce Theorem 2 and Corollary 2 which are known to complete two results on the type of an integral function obtained by him [2, Corollaries 1, 2].

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