A NOTE ON GAMMA FUNCTION UNDER THE TREATMENT OF BICOMPLEX ANALYSIS

Abstract

In complex analysis Gamma function de ned by a convergent im- proper integral 􀀀(z) = 1Z 0 xz􀀀1e􀀀xdx; z being a complex number with a positive real part. Gamma function is the commonly used extension of the factorial function to complex numbers.The analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and non negative integers. In this paper our main aim is to derive the bicomplex version of Gamma function supported by relevant examples and some of its related properties, mostly with the help of idempotent representation and Ringleb decomposition of bicomplex numbers and bicomplex valued functions.