Sum and product theorems depending on the (p, q)-th order and (p, q)-th type of entire functions

H M Srivástava ,Tanmay Biswas,Debasmita Dutta,Sanjib Kumar Datta

doi:10.1080/23311835.2015.1107951

H M Srivástava , Tanmay Biswas + Show 2 more

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https://doi.org/10.1080/23311835.2015.1107951

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Abstract

The main object of the present paper is to obtain new estimates involving the (p,q)-th order and the (p,q)-th type of entire functions under some suitable conditions. Some open questions, which emerge naturally from this investigation, are also indicated as a further scope of study for the interested future researchers in this branch of Complex Analysis.

Highlights

A single-valued function of one complex variable, which is analytic in the finite complex plane, is called an entire function
Since ε > 0 is arbitrary, from Definition 3 for the pk, qk -th order, we find for a sequence of values of r tending to infinity that
From (4.7) and in view of the first four conditions of the Proposition of Section 2, we find for a sequence of values of R tending to infinity that

Summary

Introduction

A single-valued function of one complex variable, which is analytic in the finite complex plane, is called an entire (integral) function. Exp(z), sin z, cos z, and so on, are all entire functions. In the value distribution theory, one studies how an entire function assumes some values and the influence of assuming certain values in some specific manner on a function. In 1926, Rolf Nevanlinna initiated the value distribution theory of entire functions. This value distribution theory is a prominent branch of Complex Analysis and is the prime concern of this paper. Perhaps the Fundamental Theorem of Classical Algebra, which may be stated as follows: If P(z) is a non-constant polynomial in z with real or complex coefficients, the equation P(z) = 0 has at least one root

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Mf r Mf r

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