The Journal of the Indian Mathematical Society

Abstract

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Abstract

The following interesting lemma is due to Hardy*:-

In order that φ (z) should be an integral function of order 1 and type k (> 0) in Pringsheim's terminology,† it is necessary and sufficient that φ (z) should be of the form.

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Abstract

Let†  

∑ ^∞ _p φ (n) e ^-rf(n)  (1.1) ,  (p, a positive integer),

p where s = δ + it, be a Dirichlet's series. Then the main object of this paper is to study the analytic continuation of functions represented by a class of Dirichlet's Series for which a relation of the type.

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