TITLE:
A Distributional Representation of Gamma Function with Generalized Complex Domian
AUTHORS:
Asifa Tassaddiq, Rabia Safdar, Tahira Kanwal
KEYWORDS:
Gamma Function, Distributions or Generalized Functions, Fourier Transform, Dirac Delta Function, Space of Complex Test Functions
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.8,
August
24,
2017
ABSTRACT: In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.