Abstract

The main target of this paper is to find out the estimates of the order and type of a bicomplex valued entire function. Also the famous Lucas's theorem on the zeros of a polynomial is deduced in the light of bicomplex analysis. A result is proved to show that the order and type remain invariant under differentiation of an entire function in $\mathbb{C}_{2}.$ Also we prove some results related to Hadamard composition of two entire functions in $ \mathbb{C}_{2}.$ In fact, we find out here an estimate of the type of the Hadamard composition of two bicomplex valued entire functions. Also we show that the zeros of the derivative of a polynomial $P(z)$ in $ \mathbb{C}_{2}$ are contained within the convex hull of the zeros of $P(z)$. Some examples are provided to justify the results obtained here.

Keywords and Phrases

Analytic function, Bicomplex valued function, Lucas's Theorem, Order, Taylor's Theorem, Type.

A.M.S. subject classification

30G35, 30D30, 32A30.

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